I feel like I'm uniquely qualified to comment on this, as I'm going through the IVF process with my wife currently.
> Are they more likely to find a partner as they get older?
Possibly. Maybe not, but you're essentially paying for insurance.
> That bet could be as large as a bet on the viability of the frozen eggs.
Frozen embryos are extremely viable, as long as you were able to observe their cellular division 3-5 days after fertilization. As long as you can confirm they're viable before freezing, you're almost assured they'll be viable when thawed at a later data in the future (this isn't only from my pubmed research, but also from the top fertility doctor in the Chicagoland area we're using).
> Finding a partner and raising a child on one's own both become harder as time goes on.
Disagree. In most cases, you're further advanced in your career when older, giving you more income, thereby more purchasing power. You may not find a partner, but daycare is easier to afford, or a part time nanny. Delaying childbirth most likely affords you opportunities not available to those who cut their career prospects early to have children (or who left their career entirely because they had a partner to rely on).
Also, more resources available to you means you can be more discerning about your partner selection.
> My bet is that most eggs frozen will by younger women for themselves later in life will not be used.
Its possible, but like I said above, its insurance. My wife is 30. Whatever eggs we freeze now that we don't use, they are essentially her eggs at 30, and could be used by her at any date in the future. She even has the option to use those eggs with someone else if we're not together at some point in the future (life is long).
TL;DR Freezing your eggs is an insurance policy against the future.
EDIT: Due to reasons I'd rather not make public beyond what I've shared above, I've contacted institutions who are doing research in coercing stem cells into egg or sperm cells. I expect in the next 10 years for this to be a solved problem, and the egg retrieval process to be deprecated in favor of a quick blood draw and incubation period to coax stem cells to reproductive cells. But unfortunately, this isn't solved yet.