If defenders stay back, then your offense takes a hit. It would be unrealistic to expect the team with 3 skaters to hold position against the five defending skaters. Your explanation does not hold up in that regard.
You don't get it... the zone is the entire rink in size. The defenders staying back can help possession because there is so much more space for the defenders to have to defend.
You're thinking of possession in current terms... possession would change. There is no "pressure" at entering the offensive zone, so the possession is actually EASIER to maintain - since you never actually left the zone either.
It's easier to pass around the perimeter than it is to get the puck in... the defense would stay further back, and that would still be used like you see the "top of the zone" used now... only there is less pressure on them because the defending team fears giving them the open ice lanes closer to the goal... thus the puck spends a LOT more time away from the goal while the forwards down low try to find openings.
So possession isn't harder to maintain... it's much easier to maintain, it's just harder to get an actual scoring chance.
Transition would not take a hit with no offsides, if anything there would a boost of different types of transitions. You say that teams must clear, but why would a team clear when they have 1 or 2 more players that the team attacking with 3 and keeping two behind.
I said in current rules a team MUST clear... if you get rid of offsides, they no longer have to clear, so the d-men keep the advantage, as they force the play to stay on the attack from further out.
The current offsides rules promotes transition the moment the puck clears the zone.
Example... Defenseman attempts offensive zone D to D pass, forward defender tips pass, it crosses the blue line and clears the zone... the forward KNOWING offensive player behind now has to clear the zone is now absolutely free to pounce on said puck and attack the other way.
Now, remove that rule...
Defenseman attempts D to D pass... likely from further up ice... forward defender afraid to give up ice to the D-men playing catch - doesn't play it very aggressively, because if he did, he just gives up a LOT of time/space - never gets close to the puck, Defenseman looks for further cycle options. Transition opportunity never arises.