PFS asked why I was practicing in rhythms in the first place. I started to respond in a comment, but it got quite long so I've moved the explanation here. I can see I was a bit sparing with the point of the thing in my lesson notes.
Rhythms are a good technique to use when you want to bring a passage up to speed. The other common technique is to play with a metronome, starting slowly, then gradually increasing the tempo.
What the rhythms do is increase the speed of movement between notes, while allowing time on the longer notes to recover your balance (if needed) and prepare mentally for the next short block of fast notes. By changing the rhythm, you change which fast notes are coming, and change the challenges, like shifts and string crossings - easy when slow, more complicated at tempo, but with more time to prepare.
The rhythm exercise where you add quarter notes also allows you time to hear the intonation of that note better, while you are also preparing for the largest number of notes (4) at the fastest speed.
The accent exercise improves your control of the notes at a slower tempo. Believe me, it takes control and really knowing what's coming to get the accents right, even under tempo. I found that a lot harder than the rhythms.
The bottom line is that after practicing the passage with rhythms you can play it better and faster, and better in tune. You may have noticed that between the first clip and the last my intonation improved quite a bit. I also couldn't play it at anywhere near my target tempo initially. It seems like work, but it's very efficient when adequately applied. That was my shortfall before. By changing the task every 5 or 7 or 10 repetitions it keeps your mind engaged by frequently changing the challenge.
And ola etc, I have memorized those 12 measure over 4 practice sessions. By concentrating on one short section each time, I have it memorized by the end. Then I spend 10 minutes adding it to what I've already learned, which provides the needed repetition to keep it secure. T- has a saying, which one day I will learn to spell. It's in Russian, and the translation is something like "Repetition is the mother of all learning." Remember my post about the Yo Yo Diet? A very small chunk and many repetitions is working for me.
Hope that helps.