Because they want you paying attention so you are less likely to forget changing your setup, and not just afk'ing to increase the total champ select time for everyone or miss another AFK check if the lobby is dodged.
I already have very limited time
? Are you saying the 1 second it takes to mouse over and click "Lock In" is too long?
especially with the new client being laggy.
They've made significant improvements over the course of the testing period, so it shouldn't be very laggy still. I recommend providing feedback on the Client Discussion board if your machine still can't handle it in Low Spec Mode; this is what the Beta is for. All these issues should be fixed by the time it goes live.
Also, why do I have to save my masteries before I can use them? If I don't manage to do it in time
If you don't get it in time, you tend to end up with an empty or partial tree; that probably sucks a lot more than having a wrong page selected. That is why you have to save your changes. I personally agree that champ select time is a little short for setting up a full tree and managing rerolls and trades in ARAM, but there is a ton of time in SR matches.