"considering that some pets do not work on certain heroes and you got to know only after trying em."
Easily solved by reading better... besides you can unequip a pet right away and once equipped to a new master the cooldown activates. So you have to be pretty bad to mess that up.
Also green and blue pets are pretty bad... so not much reason to switch them around, unless you can continually switch around the 7 hearts on blue pets aswell and even then all blue pet abilities are pretty much trash.
So no... 7 days for epic pet is fine. After equipping you get a free unequip, then if you equip again the 172 hour cooldown period starts, and yes, then the pet is stuck to that hero... but you have to equip a pet twice and not be satisfied with it... most pets are as straightforward as can be....
MIka: on every phys attack hero you have.
Emerson: useless garbage abilities but atleast offers a statboost... so a nice planceholder untill another mika arrives.
Jack o lantern: more trash abilities but a nice statboost and it is the only matk epic pet.
blue offers flapper, torch and anansi... anansi sucks ability wise but is works nice on heroes with a strong phys move in the 1st 8 seconds of the game... so natural fit on mirah, vulko, sarya, kong etc.
torch is the only blue matk hero so throw it on the matk heroes... ability is trash anyway
flapper is probably the best blue pet in terms of stats/boost and having a decent ability that does something most of the wave. But probably best used on heroes that make it to the point where the bonus kicks in. Octo, Malrath, Petros, Goram, mirielle...
green pets only have Falcon... he is the best green pet due to his Patk increase combined with attack speed, making him double dip into damage, however due to the under 30% activation, probably best used on phys frontline heroes, especially good on Petros.
So the pet stats are pretty clear, the abilities themselves leaves much to question... as for durations etc... but that is easy to find out aswell.