Sort of related is the story of a millionaire in Canada in the 1920s who bequeathed in his will a prize to whichever woman in Toronto could have the most babies in a 10 year period.

It went as well as you can imagine (lots of poor women having more children then they could support), followed by some lawsuits to make sure the "correct" women won the prize (e.g. not immigrants or people having children out of wedlock).

https://en.wikipedia.org/wiki/Great_Stork_Derby

It is also discussed in Act 2 of this episode of "This American Life": https://www.thisamericanlife.org/668/the-long-fuse

Eggs would be much harder, simply due to numbers. One extraction generally results in around 12 viable eggs. Even if she went through that process multiple times (not sure what repetition limits are), only 1-3 of them really have a chance to succeed through a pregnancy. After 100 years, there is little room for error.

It's an interesting thought experiment although with the unintentional consequence that you would probably end up with some of the poorest people (in every iteration of the word) taking up the offer.

You could also see some actors taking up the offer multiple times, putting up the children for adoption immediately after birthing.

Why would anyone not take the $1 million offer and end the incentive scheme?

I don't think my thought experiment limits it to a single impregnation. Multiple sperms and eggs can be used.