Having had a server setup over Plex, Kodi and iTunes, I can safely say that what you gain in convenience once everything is on there is lost with all the work you have to constantly put in beforehand.
Apple TV way.
Click home button.
Click Siri button.
Say "Sucker Punch".
Picture loads up on screen with a buy now button. Click and watch film.
Server setup way.
Browse Amazon and buy film.
When film turns up the next day or two back it up. Making sure you've unchecked the irrelevant audio laungage stuff you don't want.
Once that's done then you may want to shrink that down. In which case you'll want a half decent pc to shrink it with. You load up the film, check that it's done the right resolution, chosen the right audio tracks, checked that it's added what subtitle tracks you think it'll need. Then wait multiple hours to shrink it.
Add that into your Plex library, making sure to match it with the correct title.
At that point then you are at the same stage as on iTunes.
Click home screen.
Load up Plex.
Find movie.
Click play.
Oops. You've accidentally copied the maximum movie mode, and you've got Zack Snyder talking away on screen instead of the opening credits. And... go back and do all that again.
Or it could be Men in Black, and you start watching to find out that you've got some weird computer pop 2nd screen stuff come on 10 minutes into the movie that you didn't know was hard coded into one of the video files, and you needed to do another one instead.
Or it could any one of a number of lionsgate titles where you have literally hundreds of near identical video track files to choose from, but only one plays the films chapters in the right order. So you have to search around on Google until you find it.
Or it could be Avengers Age of Ultron where you think you've done it right first time, until you realise that 20 minutes in it hasn't picked up all the subtitle tracks, so Black Widow is mumbling away in Russian and you haven't a clue what she's saying. Same can be said for the likes of Avatar, or even films you don't really think about as having a "foreign language" like the Star Trek movies.
Unfortunately that list could go on and on with stuff like that I've had over the years..
That's without factoring in all the HDD costs involved just to keep it running.