For the duration of the fight, creatures in the immediate area will not be visible to you (but they may still attack you if they wander too close). Keep in mind that other players will still be able to see you and attack you if you are eligible for player vs. player (PVP). Other players will also be able to view your pet battle in real time, including the pets involved as well as their health as the match progresses.
They seem to have expected some things, though, see adding pets with aquatic damage (gun and ooze) aswell as a resistant cockroach to stop us from cheesing everything with elementals. Yet, a fact their damage output is low combined with shields not checking for racial damage means this mechanic prevents a lot as you mentioned. The last boss has got an ability to remove basic shields so perhaps that was not in oblivion either… unlike the reactive damage. Also, an ability that forces swap altogether with an ability which prevents from being swapped, including critters? I can't say I like it.
Most people come here not to read walls of text, they look for the better-rated strategies that match their pet collections, copy&paste stuff they need to import into their addons and only come back if something goes horribly wrong and then mostly to find help in other peoples' comments who also struggled or to find a different team/strategy: I don't think many people wanna read about stuff that already happened to them, they mostly want to see solutions and it's the best way to have them in a well-optimized strategy&team already.