I wouldn't say companies like this come and go: Infomaniak was my first (dial-up!) internet provider in 1995 and I still have my email there. Back then they used to be a small computer shop ran by passionate hackers in Geneva, organising demo scene competitions and such, and now and they grew up and are one of the biggest and most interesting internet company in Switzerland.
How about this then: Free services come and go?
Most recent example: Google Photos. Google isn't going anywhere, and neither is Photos. But free unlimited storage forever is definitely going away, even though it was _the_ distinguishing feature back when it launched.
The more you get for free, the lower the chances the provider will be able to cross-subsidize the free tier from the paid ones (and/or make enough money from ads/selling your data) in a sustainable manner.
Unlike crashing on someone’s couch, for an actually very insignificant amount (and a nonzero quantity of technical skill), you can own actually own the domain and the email server and not depend on the charity of another, and not be even possibly inconvenienced someday by the service ending when someone turns out the lights on their way out.
The cost of maintaining such a service is also minimal, but nonzero and can be an intimidating feat to attempt. The alpha nerds will beat their chest and state that they are so technically inclined that this approaches zero for them.
I believe the worst problem here is spam. Google grew that much as email provider also because they have among the best filters out there, but what about different servers on small hosting providers? Security issues aside (I assume their sysadmins know how to setup a safe email server), I've planned that route many times and resisted because having to fiddle with constantly changing spammers lists is something I really wouldn't want to waste a minute on.