I would think it depends on where in the crossover the electrolytic capacitor is. Depending on the location as they fail you could end up with drivers not receiving as strong of a signal as they should or getting frequencies that aren’t ideal for them to be trying to reproduce.
Replacement capacitors can have different effective series resistance which will also affect the crossover.
The downside of replacement is if you are thrilled with the sound now that may change.
On my 20 year old speakers that had an electrolytic in line with the tweeter there was a noticeable improvement in the high frequencies. Now, I don't know how much of that was form a half ohm less resistance.