Things obviously change.
Interesting, as I only flew 707s and 747s in the early days of autothrottles. Putting out spoilers in cruise then increased thrust if the A/T was still in. So you wound back or disconnected the A/T first. Your point about spool up times is valid, but if you anticipated the target speed you could easily spool up in time and flight idle rpm took spool up times into account. In a severe slowdown you still reduced thrust prior to spoilers but not necessarily to idle depending on the situation. Using spoilers against thrust was a no-no.
Undoubtably with better computation over time this has changed and the deployment of spoilers adjusts the thrust appropriately so that it's not working against the increased drag. You are correct with the Boeing terminology re "speedbrakes", but its mostly a simplified convention. Speedbrakes don't give you 'walkdown' as airline spoilers do? (did).
In most fighters you want to reduce speed quickly without reducing lift and turning performance, so you hang something out that's usually off the fuselage and not the wing. For airline purposes the distinction does not matter as Boeing has decided and "speedbrake" is the simpler generic term. However, it would be interesting to know how much the later Boeings' stall margins are affected by "speedbrake" deployment compared with the early models. No doubt the airbuses are similar to the later Boeings so I accept that speedbrakes are now the first option. I'd also be interested to know how much the lift dumping function relative to the drag increasing function of airliner "speedbrakes" has changed over time. No doubt it varies with the phase of flight whereas earlier it was one size fits all. Thanks for the correction.