Why would either of those be backgrounded? Neither of them involves a town. A rope bridge, obviously, would be part of adventuring, so, a companion wouldn't be backgrounded. Or, if the player did background the companion, then he would not have that companion available until he or she returned.
Note, it's not about making the T-rex town friendly. It's not. It's that instead of spending table time hiding the T-rex every time you entered town, you'd just take it as written that it is hidden and won't get into any trouble while you are away.
It's not a dodge at all. It's simply taking an element of the game that isn't particularly interesting to the player and just taking it as written. But, again, it does cut both ways. If you background something, you don't get to use it while it's backgrounded. So, a backgrounded T-Rex that gets taken into town isn't backgrounded. It's very much foregrounded and all the consequences that go with that are on the table.
See, here's the thing. It's not an interesting choice to the player. It's just not. But, it's also not a power gaming move either. A backgrounded spellbook couldn't be used on an adventure. Once it was used, it's no longer backgrounded and it's fair game. A cleric that acts obviously against the intent of backgrounding his or her class - the whole undead menagerie cleric example - is obviously acting in bad faith.
Why do you assume your players will always act in bad faith? Why do you feel the need to police your players?