actually you can also open a desktop wallet on your smartphone if you open myetherwallet you can access it via google chrome, but if you want to access it more easily you can install the Imtoken application on your smartphone.
Actually there are many crypto wallet these days for storing your crypto coin. I’m using trust wallet, imtoken, and of course myetherwallet. I'm using these for long now so far I did not encounter any problem and also good for newbies. Let us just always lookout and be safe of our private keys not to share anyone.
does myetherwallet have a mobile app version?
I have never looked for it in an app or plyastore because I was used to using the web if I wanted to access it.
the rest I use trustwallet and other applications to access the wallet directly because it is automatically logged in or synchronized with our wallet, when we first connect.