Pretty cool system.
Correct, in case blockstream stops giving service you would only have to restore the seed in another wallet or operate in the other mode that Jade has which is air-gapped (like seedsigner).
There is no risk of loss of funds.
On the other hand you can set up your own server:
https://help.blockstream.com/hc/en-us/articles/12800132096793-Set-up-a-personal-blind-oracle
You also have it on Umbrel:
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