Naive me would expect that these are typically lease agreements whereby the OEM promises an SLA with compensation if they have to take the aircraft out of service for design issues? If they don't do it that way, why not?
First, because taking aircraft out of service for design issues is incredibly rare (less than once a decade across all kinds of passenger aircraft).
Second, because airplane manufacturers have a significant amount of negotiating power, combined with airlines very often not being in a great financial position: Boeing certainly wouldn't want to be liable for storage costs and the logistics of getting a fleet of planes back to a central facility if an airline went bankrupt, for example. Leases also get legally interesting when the assets involved move internationally on a daily basis...
I wasn't proposing that any of that and I'm not sure it's relevant (e.g. in this case it's a software update that can be done without moving the plane); I agree they wouldn't want to take over a dead airline, and such an agreement doesn't get the incentives right. But it's common for OEMs to take the hit for things that are their own fault, if it isn't legally required.
And the rarity of the incidents plus Boeing's asymmetric knowledge of them would favor Boeing being a guarantor. And remember, I just said the design issues. Obviously the airline would be expected to take hits from e.g. FAA groundings from their own maintenance failures.
Edit: That leaves asymmetric bargaining power in your reply, but I don't see OEM aircraft competition as being so monopolized that they wouldn't compete on "hey this company makes us bear the costs of their design problems but this one doesn't".
Only one airline has a fleet of more than two dozen 737 MAXs (of any variety) currently: Southwest (and that's only 5% of their fleet). There are essentially no airlines with large fleets of them yet, which makes this relatively easy for them to deal with.
That said, "relatively easy" is still a comparative: aircraft are frequently leased and having any out of service will be costing the airline a lot of money.
Depends on how big the airline is, what percentage of its fleet consists of max 8s, etc.
Generally, planes like this have high operating costs, and usually are kept in the air pretty much constantly to be able to make a profit. Having one grounded potentially means losses of hundreds of thousands of dollars a day.
IANAL, but I would not want to deal with the headache of underwriting whatever plan you're thinking about. Who would they be buying this insurance from? What specifically could it be protecting against?
Seems much more likely that they'd need to seek restitution against the producer of the planes through civil court channels. "You sold me a faulty plane/didn't explain what your product did well enough and now you need to refund my money" but on a multi-million dollar scale.
Insurance for loss-of-use is quite common (edit: in other industries—no idea for aviation), though it's normally (AFAIK) for natural disasters and other random occurrences. I wonder how the purchasing contracts between Boeing and the carriers are structured—perhaps they have a warranty that would do something similar.