The PM has a constitutional duty to stay in power until a replacement can be appointed (like Gordon Brown did in 2010).
So, if May should have had the 'integrity' to resign, you would have to consider one of the following to be morally superior:
1) Prime Minister Corbyn
2) A new Conservative Prime Minister
3) A new election
You'd only get Corbyn if there was another election, and I doubt many people would have the stomach for that, so therefore it would seem that a new Tory PM would be the answer, although exactly who I wouldn't like to predict, although I doubt any of them could be worse than May.
As for May does he really think her arrangement with the DUP is not a disaster. She is playing with fire she risks the breakdown of the peace agreement in Ulster. Also agreeing to give all that money to prop up the Tories is beyond belief.
All it has done is to confirm that she will do anything to keep the tories in power she is devoid of any moral authority.
I go along with all of that LB, and her calling an unnecessary GE primarily to boost up her own authority showed a complete lack of judgement, and now that that's backfired she's compounding this by forming what I see as a rather dubious alliance, even if it isn't that in the true sense of the word. In fact she's so incompetent I wonder what she'll cock up next, particularly with the Brexit negotiations.