Would you like a repeatable mission to grant Rift Fragments?

I don't know, there isn't a whole lot you can do. Also, chances are you'll be done with the Rift if you completed all challenges (you earn RF from the XP gained too).

Maybe you could get a fragment bonus after you complete Level 4 of the Tome?

This is just not true. There is a serious post-tome grind after you've finished all the challenges, not everybody knows this because they don't like to actively go out of their way to change their playstyle, do all the challenges, yadda yadda yadda but I do.

Doing all the challenges as a normal human being (who has a decent amount of time to kill on weekends and some spare time on weekdays) who isn't a huge pro at the game and doing all these challenges in a reasonable amount of time (you won't be finishing them all in one match, and you might find some difficulty with specific ones that you can get stuck on, so you'll be playing multiple trials gaining xp without necessarily finishing a challenge each trial).

ALL that being said, the challenges in the tome take you about 85% of the way there. Most of them finished and only a few left will get you to about at least level 60 (out of 70), this particular time around the challenges took me all the way to level 65.

I don't know about you, but Post-Time grind is absolutely god awful. When you're not playing for yourself and you're just grinding because you're on a timer with a finite amount of days, I had to ignore friends who wanted to squad up in other games for multiple days in a row (and obviously this annoyed them a little bit), and go out of my way to get the tome done because the challenges don't take you all the way.

It's a seriously long slog through the last bit too, you think "oh, 5 tiers isn't a lot, you already made it through 65" Yeah, 65 with the help of the triple and quintuple fragments I was earning from normal and master challenges. Doing it purely off of your own xp in your matches is absolutely terrible and it takes so long.

Breaking it down: It takes 800 xp to earn a fragment, playing average game where you don't DC or die early (if you're playing survivor) nets you around 400/500 xp this can last around 10 minutes maybe a little bit more or a little less. Playing a sweaty game where you go all out and you get a 4k as killer or play really well pop a bunch of gens, save a bunch of people off hooks, make your chases last, etc. and escape as survivor, games that definitely last over 10 minutes long. These net you roughly 900 xp. So in layman's terms, it takes you about 1-2 matches to earn a fragment, it takes 10 fragments to complete a tier in the rift. So for 5 levels, you're looking at a bare minimum of 50 matches and that's if you're going sweaty every single game getting 4k's or escaping and if you're not getting either of those you're at least playing really, really well. Which is obviously unrealistic, so it's definitely going to take most people over 50 matches to do this, but say it was 50 matches, 50 matches that lasted exactly 10 minutes each. That's 500 minutes, divide that by 60 minutes per hour and we're looking at roughly 8 hours and 20 minutes of pure sweaty tryhard matches, for most normal people who just aren't going to go full sweaty tryhard just tack on a couple hours (because 1 - 2 matches for a fragment worst case scenario you're playing 100 matches, so 1000 minutes so 16 hours or just double the minimum time)

Now, 8 hours, in gamer terms, isn't actually that bad that's maybe one full gaming session where you're gamin' out all day, on DBD. Nothing new, plenty of people do that, and if you wanted to you could break that up over a period of 2 days so four hours a day. It still doesn't change the fact that none of this is FUN, that's what all this math adds up to it adds up to "not fun".

TL;DR

The grind should be to finish all the challenges, finishing all the challenges should finish you the rift and that's it. That being said that's not the way it actually is, so I would more than gladly welcome a repeating challenge, something that earns you fragments over and over in the mean time. It could be a little separate bubble in the top right of every level of a tome level 1's repeating challenge is easy but only nets you 1 fragment, level 2's is a bit more difficult but still doable so you get 2 fragments, 3's is a standard daily challenge which might be difficult for some so you get 3 fragments, and level 4's repeating challenge is a true master challenge that actually might be pretty difficult, but it gets you 5 fragments like all the other master challenges. I would absolutely wholeheartedly welcome this feature, and if you don't you're an absolute fool who is asking for the grind to be longer than it should be without ANYTHING to actually do once all your challenges are done.

Lol thanks, I really do hope they do something about that post-tome grind. Your idea / suggestion was a good one