There are multiple reasons why there is no "Run all tests" feature. For a start there are a number of tests which are mutually exclusive - some people want authors FN LN, others want them LN, FN. Some people want metadata jackets, others hate them. Other tests may be of no interest whatsoever as not being something you care about. So such a feature would need to have the ability to run a selection of tests rather than all.
The next problem is that many of the tests can produce "noise" - false positives mixed in with the genuine books of concern. So a "Run all tests" would produce absolute reams of output which would swamp users missing the wheat from the chaff. I recently added the ability to specify exclusions for a test which might be extended to help but it would force users into using them.
There is also the amount of time taken - as the tests I have added have gotten more complex (including scanning the content of each html page in an epub for instance) so has some of their running times.
The biggest issue by far however is working out a UI to trying to present the results of these tests. Producing some giant report wouldn't be very useful and painful to try to work with. Stepping through one test after another would be very long winded and painful. I haven't given it much thought because it all involves much pain.
With all that said, I do see some value in perhaps offering the ability to produce a summay report for a selection of tests. It would run all the tests and produce a summary (might just be a simple text log to begin with) that would tell you how many "issues" you have after running each test. You could copy that to Notepad or whatever and then individually run just those tests which showed issues you were interested in and resolve or exclude them. Note I am just thinking out loud here, not promising to implement!
In answer to your other question about where to start - well it depends on what is of interest to you and that may evolve over time as your library gets progressively cleaned up. Personally I would start with your book metadata (in conjunction with the Find Duplicates plugin) to make sure your titles, authors and series are rationalised/correct. If you don't care about stuff like comments, publishers etc then simply don't run those options (or leave them to a later iteration).
Then presuming ePub formats are your key master format ike they are for me and many others, start hitting some of those options and if desired use the Modify ePub plugin to fix them. Personally the only ones I use regularly is to identify/remove <address> tags (since they screw up book formatting) and remove metadata jackets (as they look fugly).
Just experiment and have fun with it - there are no rules about how OCD you have to be about your library, the plugin should help with a range of obsessivenes...