There is still a full-term Governor running. Trump would make a big mistake if he considers any Governors as running mate, except for those that had the good sense to step down before they got completely sucked in.
Kasich is a sitting governor who has a job to do that the people of his state hired him for.
He only one his state, Ohio, and has lost 41 other contests.
He has no path to victory. The only person who could possibly have helped him block Trump (which was unlikely in any case) has suspended his campaign and dropped out.
Donald Trump is likely now to get almost 1,400 delegates on the first ballot.
Kasich staying in at this point is not only foolish and pointless, it is an absolute disservice to the people of Ohio.