If you make your booking early enough then you stand a reasonable chance of getting the date you want - you might have to travel but otherwise shouldnt be a problem.
But, there are a couple of reasons that I can think of that would make it not a great idea to deliberately book on the last day.
You could be sick and no chance to delay. There maybe strikes or IT issues like this year which mean you cant do it. There would be no flexibility if something went wrong on the day. You would have to wait a year.
Also one of the key benefits of the Ucat over BMAT is that it allows you to be strategic. Doing it on the last day only gives 17-18 days or so to work put where you are applying, review their application processes and policies and target your PS to those med schools requirements (if they look at them) complete your ucas forms and get all your references sorted etc.
Could put a bit of extra pressure on.
Good luck whenever you do it.