Actually... No it wouldn't...
Think about how a regular control point map works. Just set a few control points in the map, and add time when a point is capped. Make sure that the round does not end until every point is capped or the end of the map is reached.
I don't feel like it would be any different than the current timer, if anything it would encourage people to proceed through more of the map.
Instead of 7 minutes, the map could be split into two 3 minute section, and one 1 minute section (as an example). It would encourage people to go through all the traps in a timely manner instead of just sitting at the beginning of the map and waiting until the last bit of time to go through everything.
Honestly, I had a more compelling argument for why I thought this method would be better than just a straight up timer, but it's not coming to me at the moment.