I develop my web applications using only PHP for the view files and I don\'t feel limited in any way, but I hear there\'s a consistent number of developers advocating \"external
First addressing the answers on here and the general background:
The primary reason people use them being is that that they usually make things a little more terse. It's questionable as to whether this is always a net benefit. The increased cogantive load of learning a new language and not having the flexibility of your host language at hand can eventually end up offerring more drawback than is offered by using a templating language. Twig in particular requires manually exporting core PHP functions to it. The best templating languages that seek to be terse would be better off instead extending PHP using the tokeniser.
Automatic escaping is another questionable feature. For a developer that codes very poorly, automatic escaping might be more secure but otherwise it weakens security, putting it out of mind and presenting the expectation that everything will be secure by default in any context. A really secure templating engine needs to know a lot about its context, sometimes this can't always be determined, only the programmer knows where something goes. If you need secure programming you need to have a developer that is not reliant on automatic escaping, period. This is also something that PHP actually can do, if you tokenize the PHP file you can separate raw text from PHP and wrap the PHP parts in output bufferring then apply any filter you like, so this is not a templating language exclusive feature.
Some templating engines can make pregeneration a bit easier and pre-compilation to make them faster, but this can be achieved with native templates as well. There's a necessarity to parse templates which often makes them less efficient and the process more complex for using them. The added complexity templates introduce is significant. This can often be abstracted away from you but will eventually come to bight you, for example caching issues (stale entries), performans issues, significantly more flutter and clutter when debugging, more layers and more code being excuted with much more that can go wrong, etc.
Many features such as extending templates you again do not need to use twig to achieve that. Similarly for things such as htmlspecialchars most people will create short helper functions for all of the functions they are using very frequently.
So where should you definitely use templating languages such as Twig?
Baby sitting bad developers is sort of valid, although I'm not sure that they should be considered developers if you have to use something like twig to try to contain them. You'll also miffle good developers you'll wonder why they are being made to jump through hoops to achieve otherwise simple things.
You might want to give templates to parties where you might want the HTML to be worked on but to not expose system internals, etc. This might be where you have a CMS for example, with users that can edit templates but are not the same as your developers. This related to the above but it's a more genuine case where you might have some benefit and that might be justified.
A similar case is where you might want to use templates between systems, in this case a templating language can be a portable solution. This might not only be where you have multiple backends but where you have unusual architectural requirements such as the forward facing servers rendering views from data derived downstream. Take this further and you might want templates you can render frontend or backend. If you only have to ship data to frontend because it can render views itself, this can be more efficient. However you may also have to fallback to backend for various reasons.
Another case is static analysis including across multiple languages. Most languages template effectively by string concatenation and arn't aware of the language you're producing. In some cases a templating language can provide a benefit when you can parse it fully, the language and the HTML. Another way to achieve this is to do your templating using HTML itself as much as possible to denote things, as in using classes, etc and the facilities HTML provides that can allow you to attach behaviour to things. A templating language can also be more parsable than PHP even if you're not able to also parse the language you're templating in. This can be used for optimisation or having templates that are more easily transpiled.
Your language really isn't suited to creating HTML and other languages. PHP is a templating language so in most cases the use of a templating language does little but incur substantial drag. However if you're using something such as Java then you're very likely to desire a templating engine. Templating languages are a DSL, but if you already have a DSL that does what they do pretty well then it's YAGNI.
Bespoke templating. Where you have a certain output format and domain that would significantly benefit from a customised templating language. This depends on your output format.
All of these cases are situation specific and not sufficiently common that a templating language should be used by default. Templating languages only address these points with varying levels of success (for example, many aren't HTML aware). If I were to rank Twig 10 out of 10 for how well it does each the average wouldn't be far off 5.
You can convert Twig into PHP but not PHP into Twig. This can sometimes be useful but it comes as a considerable cost as you lose a lot of the flexibility of PHP.
Of the small amount of Twig internals I've been exposed to the quality has also been poor, or has imported bad standards. For example the parser doesn't or at least didn't support perserving whitespace when I first tried it five years ago. I had a scenario where I needed to refactor, which meant I needed to be able to parse Twig, modify and output it again to rewrite code across thousands of templates, twig didn't support it and I had to rumage through the parser myself.
Similarly I recently investigated escaping for Twig. In particular the JS escaping stood out which supported escaping JS strings and other strange things rather than simply using json_encode. It's likely the custom escaping you'll get like that in frameworks is wrong. It's usually more reliable and secure to do it yourself (as long as you know about things like what happens if you JSON encode a string containing and template it as a javascript literal without sufficient escaping, for example).
In most cases the hundreds, sometimes thousands of lines of magic templating systems and other related systems implement for escaping, sanitising, etc are terrible practice, trying to guess your scenario or trying to cater to every possible one, adding more scope for bizarre bugs with data corruption, adding more chance of security blunders, etc. Usually you'll find the things like that in frameworks can be replace with a one or two line function that's more secure. You'll have other silly things as well sometimes like processing something over and over just in case because the framework is naive as to what you're doing where as if you make the things yourself you know exactly what you're doing and don't then have things like ending up sanitising the same string over and over.