There should be no debate about this really. Whatever problems people had setting up Cloudflare in the past are long gone. It is amazingly simple to set up, offers major security advantages even on the free tier, and drastically speeds up any phpBB forum.
Any CDN will speed up a phpBB forum, but many CDN services
How much you benefit from a CDN will depend on where your server is located and where you primary audience is located. If there is a significant geographic distance between the 2 or you have a global audience, you will notice massive speed improvements. In my case page loads decreased by approximately 2 seconds.
By default Cloudflare only caches static content, so the fact phpBB serves dynamic webpages is quite irrelevant.
Caching do not cause any issues in practice because phpBB now implements versioning of all static files. If you make a change and purge the cache, the version number query strings will automatically update and Cloudflare will, by default, recognise the query strings and invalidate the previous cached version without requiring any user intervention. The only exception to this are CSS files which are called using @import from stylesheet.css. Unfortunately this practice breaks versioning and you need to reversion those CSS files manually.
The main issue with Cloudflare on phpBB is passing on user IP addresses. That is solved with either a simple code change or using of the 2 Cloudflare extensions (both of which are virtually identical in operation and simply apply the code change that can be applied manually).
However, Rocket Loader can cause issues where there are JS dependencies and they are not loaded in order. In my case, it did cause some issues with ad banners. These issues can be resolved, but would require some manual tweaking to ensure scripts are loaded and executed in the correct order (or bypassed by tuning Rocket Loader manually).
The single greatest advantage of Cloudflare though is being able to block bots and malicious actors before they even reach your server. Even on the free tier, you get 5 Firewall rules and you can stack these pretty infinitely which allows a lot of flexibility in what you can do. A single Firewall rule might list 20 user agents, 20 countries and 20 ASNs you want blocked. In my case, I have a Captcha challenge shown on the registration page and I can see the percentage of users who have been able to solve it and which users are being blocked.
Finally, Cloudflare domain renewal fees are at cost price and the DNS is very easy to set up. When you make changes, they propagate virtually instantly, compared to some of the conventional DNS players where it can take 24-48 hours to propagate a change.
In summary, Cloudflare is fantastic and I highly recommend it.