It could have, sure. That would have been easy. But it would have added weight and complexity. That would have reduced speeds and/or altitude and/or range between in-flight refuelings.

We fixed it the other easy way: In the event that an SR-71 makes an unscheduled stop somewhere that wasn't prepared for it, then we send out a bunch of dudes with a cargo plane and some starter carts. That just takes money, which even easier.

It also takes time, but time was not a big deal: The plane was going to be there for awhile anyway. It could go over 15,000 miles between takeoff and landing; it wouldn't have landed where it did if it weren't broken somehow to begin with.

It'd need repaired by the crews who actually knew how to work on it -- who would also need flown in.

It would also need fuel before it could leave. That's problematic since the JP-7 it required was shared by ~nothing else in the sky, so: More deliveries.

Waiting for some Buick V8 starter carts to be delivered from the other side of the world wasn't really a roadblock at all.

There's a bit in the Skunkworks book that talks about added weight costing significant altitude. I don't have my copy in front of me but it's quite a severe tradeoff: some fairly small amount (100kg perhaps, might even have been less) reduces ceiling by 1,000'.

For military planes, every bit of weight you can shed up front increases some operational capability of the plane. In this case, not carrying an extra 200-300kg of weight for starters meant 200-300kg more spy equipment /could/ be carried along on the mission.

Most jet planes do carry a starter with them (in the tail usually) so the fact the SR-71 doesn't suggests the tradeoffs wasn't worth it

They would have to make the plane bigger. The SR71 is already an enlarged version of the A-12, made bigger to support more fuel, a heavy camera, and an extra pilot. It needed something like 900lb-ft torque per engine; even modern electric motors would add enough weight that it would be problematic.