@cleeds
What you are missing in your understanding is that the filter sections for each driver are independent in the classic, parallel crossover.
When the external straps are removed the individual high and low pass sections remain in place but the crossovers should not (and usually are not) have any be connected internally.
An external crossover would of course be additive to the internal crossover so it's not quite as good as having a purely external crossover, but it's workable.
Still, the risk of connecting two amps to the same bi-wire speaker is only present in rare cases when they join the grounds internally, and a balanced amp is used.
Best,
Erik