The question of the spawn mechanic is not trivial, and can be asked in the case of circular capture point mode as well.
There are many possibilities for the spawn attribution.
->closest to
->oldest point owned by the team
->newest point owned by the team (the one currently applied)
I discarded the oldest point one, but it does have its advantages : it focuses heavily on the defensive side, because, until not lost, the oldest CP can serve as fortress, while the pushing team must go farther and farther. It allows engies to use teleportesr, since exit may stay stable for a long time. But at the same time, it creates an unusual situation when one team is ahead : the winning team must cross the hostile cart to reach theirs, in something like this :
RC--->BS--->BC--->RS (RC and BC are the carts, BS and RS are the spawns).
Red players coming from RS, have to go along the rest of the track, or run straight through the blue cart and the blue spawn, to help pushing.
Whereas in the newest CP mechanic, this cannot happen. When one teams takes the leads, here the situation
RS--->RC---->BS---->BC. Red players wanting to stop the blue cart may go straight and have to passe beyond the blue spawn. But it's not very important, since they were seeking fight anyway. And a good defense should be entranched somewhere in front of the road. The main issue is teleporters aren't used, because a good team will lose its current spawn quite often. Moreover, spawning players are always in situation of "pushing" their cart, instead of ending in situation where they have to "pull" it.
And finally your proposal creates another type of situation. The main issue is whereas taking a point and triggering a new spawn is something very understandable by players, "closest" attribution would be more obscure.
Maybe this topic would require another thread, dealing with unusual gameplay mechanics.