It’s their system of government and it has generally worked well. She would not be my choice, but she is not going to be President. She is going to be the leader of her party which also holds a majority in Parliament.
And it’s also worth noting that Winston Churchill was never elected Prime Minister during WWII. He got the job the same way May did. The then PM Neville Chamberlain lost the support of his party and realized he had to go. The choice for the next PM was between Churchill and Lord Halifax. Chamberlain called them into a meeting and asked them whose name he should give to the King to form the next government. Halifax bowed out saying that as a hereditary aristocrat he would have to govern from the House of Lords and he believed that was not possible in the middle of the 20th century. He then said he thought Churchill was the man for the job. To which statement Churchill agreed.
And that was that.
“Well, he would, wouldn't he?" - Mandy Rice-Davies