I think exploring all warranty options is prudent, especially any that might still be valid for the pool. But I respectfully disagree that a home warranty "isn't worth it," even if it isn't going to help with the pool situation.
First, home warranties are often included in the purchase of a home, paid for by the seller. I'm surprised your realtor didn't fight for this. I renew my warranties on my rental properties and they rarely don't pay for themselves each year (sometimes many times over). My best example is the warranty on a unit that had an old heater/ac unit. It went out, and while the warranty didn't cover every expense of the repair, they did cover all but $1800 of an $8000 new hvac unit!
More to the point: the owner, and the owner's realtor, should have disclosed that pool crack to you. The owner surely knew about it. The realtor should have included in the paperwork his/her own general inspection of the property and that, too, should have disclosed the crack to you. So something fishy is going on here. You mentioned there were a lot of things to repair, and the seller is not willing to negotiate. That's fine, that's not unheard of. But if this guy is willing to try and hide such an expensive and obvious disclosure to you, then you might be, um, sorry, foolhardy to think that this is the only thing he's going to be hiding. Anywhere from bad/illegal repairs to known faulty construction to who-knows-what. Was the house freshly painted? Can be a red flag, as it is an excellent way to hide all kinds of things.
The same property I described about the hvac was hiding a $30K plumbing replacement project that has since necessitated numerous repairs. Because I live in a small town, the plumber I used for the stop-gap repairs was very familiar with the property and had worked on the plumbing many times, and advised the previous owners, years before, that the plumbing was shot and needed to be replaced. No disclosure. I decided not to pursue legal action (it would be all very hard to prove) and do the repair myself, for about $3K in materials. Plus, I had the assurance of it being done correctly (by me!).
How old is the house? How much in love with it are you? How prepared are you for a money-pit scenario, which is already unfolding itself in front of your very eyes? Sorry, a little tough love here. Maybe you'll be offended, or maybe you'll appreciate hearing this? If you're in escrow, I doubt very much you can't still call all this off with no money lost (save the inspection fee).
Is this house such a deal that you can afford to potentially be repairing it for years to come? You've already said you're strapped. How many hidden problems is it going to take to get yourselves into real financial trouble?
I'd double down on inspections and have more things checked. Roof for one? Did your home inspector do the typical walk around and fill his report with legalese to the effect that he wasn't able to inspect this or that and you should pursue a more thorough inspection for such things? My report was filled with those types of liability-escaping clauses. Some of these guys are just plain lazy and rely on cleverly worded contracts to keep themselves out of future troubles. But at least my guy crawled up into the attic, up on the roof, etc. Did yours? Mine still missed several very expensive repairs, and those on a 5-year-old house! Something I do for new purchases is take a trip to the building dept. Have them pull all the records on the house. Sanitation dept, too. Any county/city dept that maintains records on residences. I uncovered a $20K septic system repair need on a pending property that was not disclosed otherwise, and walked away from the sale. It later stayed on the market for many months, and finally sold later for about $50K less than my realtor offered! The seller is messing with you, and holding out hoping you're going to cave. Have you threatened to walk if he doesn't discount for repairs? How else will you know what he is actually willing to pay for? I know the CA market is tough. Were there multiple offers? Are you so sure someone else is willing to buy this place at the price you've offered?
Realtors, sellers, inspectors, they're all supposed to be, to some degree, on your side in terms of understanding what you're getting into. But they all have inherent conflicts of interest. You have to proceed as if you're on your own (which, for the most part you are)! I forget the term for it, but it's common enough to have one. Refers to the state that buyers get into during escrow, causing temporary blindness to things that would otherwise be obvious.
IMO, you should think long and hard about this purchase and proceed with great caution. Ask for an extension on the escrow to investigate further. At the very least, insist on a warranty paid for by the seller. Buy it yourself if you have to. I know this is not what you came to TFP for, or what we do here, but I felt I should say something. Again, sorry to be so rough on you...
Good luck!