Let’s keep this to the open era, nothing before. Oh, and I guess we can mention both men and women, though I have mostly been thinking about the male players.
I think the most obvious answer would be Thomas Johansson. I don’t think he is a bad player, but he was not someone I expected to win a major. His only win was the Australian, and Marat Safin basically collapsed and gave it to him.
I wouldn’t even know where to begin with the worst woman, though.
In terms of rankings, Johansson peaked at #7; Gaston Gaudio peaked at 5, and Albert Costa at 6.
Titles: Johansson 9, Gaudio 8, Costa 12
Other tournament results: Johansson SF (Wimbledon); Gaudio Fourth round (other French opens, several times; never better than third round anywhere else); Costa SF (another French open; managed a QF in Australia).
I’d give it to Gaudio.
It’s actually pretty hard for a mediocrity to luck into a title in tennis (at least as compared to say golf as I’ve said before). Limiting myself to the open-era, for the women I’d probably put down French Open champs Anastasia Myskina, Iva Majoli, Virginia Ruzici (all clay-court one trick ponies) for starters. Chris O’Neil (Aussie Open '77, her only career title) is one of the few who came out of nowhere and promptly disappeared back into the void.
Petr Korda comes to mind, if only because the tested positive for performance enhancing drugs a few months after winning his only major (Australia in '98). He did have a solid career with 10 titles and I think he lasted longer than Gaudio. Myskina is a pretty good choice. Her career was humming along for a while, but she won the French Open even though she’d typically played poorly on clay, and that year’s final was terrible. (She won 6-1, 6-2.) She was already mentally shaky and within a year or two she’d fallen apart.
Brian Teacher, perhaps? He won the 1980 Australian Open, but never made the finals of any other major tournament, and never was ranked higher than #7 in the world.
Mark Edmondson is another possibility.
If you are going for Australian Open, there are a lot of obscure winners, many Tennis Players could not be arsed to travel there to play until almost the mid nineties. Connors, McEnroe, Borg etc. Even Agassi did not play for the first 8 years of his career, which must annoy him everyday.
OP: Yes hard to go beyond Johansson and Gaudio. But then both won because of metal collapses by their opponents, Safin and Coria (who incidentally was in the final due to a similar mental collapse by Tim Henmen).