Pros

- Strong team fight potential
- Mid game damage is reliable
- Very useful ability set with slow/stealth

Cons

- Short range
- Lane phase is unreliable
- Requires a good team to set up fights

The main reason is because it's fun to use, but another good reason is because it's especially effective if you counter the opposing adc. It is also a very strong snow balling build.

If you have a Lulu and a Yasuo on your team you can stealth in the middle of a group of enemies, have Lulu ult you and get a follow up from Yasuo. You won't always survive this tactic.

The so called 'submarine' is where you have Shen ult you while you're stealthed behind the enemy team, this can be followed up well by a nocturne/orianna etc.

I do not recommend the Ranked 5's Purge build for use in solo Q as it relies heavily on you staying alive for extended periods of time without the use of defensive items.

In Solo Q Twitch is a weak laner and a strong assassin, if you play him right you can turn fights using your ultimate, you just have to position yourself well.

If you do play Twitch in solo Q I recommend you have a support duo with you.

Twitch is a lot easier to play in Ranked 5's than solo q.
Having your support duo with you will help your lane.
Play safe in the early stages of the game.
Position yourself well to get a good ult off.

Have a nice day and stay away from edgy memes.