Wow, that looks good! That's how I kind of wanted the page to be like.

Thanks.

Also, why do we need algorithms that don't preserve F2L? Parity is usually peformed after F2L, so algs that mess up F2L are useless really.

Well, I don't see any real use in algs that don't preserve F2L either, but the algorithms I found in the past like this (and even more importantly, cuBerBruce's algs which are currently posted on that page, well, except for three which I found) are, I guess, just interesting. I mean, the 15 BQTM algs of cuBerBruce's are pretty neat. Besides some individuals using, say, the second (17,13) algorithm for Petrus, I guess it's important to have these algorithms posted in the wiki because it gives everyone appreciation for the standard algorithms which preserve more and are only a few moves longer. I'm sure you have seen the parity threads that have gone on, at least in the time I've been a member. On more than one occasion, people were wondering if there is a possibility of shorter parity algorithms to exist. I mean, we don't have an official cube explorer for the 4x4x4. cuBerBruce has done some impressive work to get around this, and I of course have done so on many levels myself (which I feel privileged to do for my fellow cubers, and I'm sure cuBerBruce is very proud of the accomplishments of his brute force searches). I guess at the end of the day, we (and whoever does constructive writing and/or makes contributions which make it on this page in the wiki) should hope that we provide speed optimal and move optimal solutions of all kinds so that everyone's needs will be met, whether it is for practical use in solving, curiosity, a look into the theory, or just to have a deep appreciation for the parity algorithms we have.

And just as an example (not that you mentioned algorithms for the checkboard pattern 4-cycle), but...

Even an algorithm like

[f2 u' r2 Uw2 S': r] has its purpose (besides being the optimal algorithm BHTM and BQTM, we can still learn from it). As I have posted on the comments of a youtube video, if anyone wants to argue that parity algorithms are unintuitive, they should study this algorithm

[f2 u' r2 Uw2 S': r] and reconsider. It doesn't matter how many moves it takes you to get slice r to look like it does after f2 u' r2 Uw2 S', as long as you can make slice r look like that, then you're in business. Simply observing how same color centers swap with each other when the extra quarter turn is finally ready to be executed is such a simple concept, it's beautiful. When I started cubing, and even after I found optimal solutions to various cases in different move metrics, I was always thinking to myself, "there must be a simpler concept of how to handle parity, even more so than my methods." I didn't find this algorithm right away (heck, I just found that early this year!), but the idea behind the algorithm is so simple that, once a cuber sees it and understands its one message, then the fear of parity should vanish forever. Easy to understand parity algorithms for, the pure edge flip, for example, clearly do exist:

[f2 u' r2 Uw2 S': r] [Rw: [U' f' U, B2] ]. Sure we can just do a quarter turn and then solve back everything, but that's not really looking at the problem head on (at least, not to me. That's just doing something to bypass the "big problem" of having deal with the consequences of an odd permutation in the inner layers. That approach is like saying, "since my computer program has a bug, I'm going to start over," instead of trying to debug the code and actually learn how to prevent mistakes like that from happening again).