Is there a drawback to switching active households frequently?

It may lead to a bigger save file size. Bigger save file means it's going to take longer loading. There are ways to clean up a save file. First things first... turn off memories via in-game options. Memories clog save files.
This guide shows how to use Save Cleaner will do it for you... V2.2 for patch 1.67 & below

Save Cleaner V1.1(direct link) for patch 1.69 since V2 doesn't work with the last/latest patch


Tips For Better Game Performance

If crashing occurs, I would make sure the save file isn't bloated or the game isn't hitting memory cap first. (3.7GB for Windows & 2GB for Mac - you can track this in task mananger)

Even though I don't play rotationaly, it's not going to blow up your game doing so. :) Just the normal concerns any player runs into. Playing rotationaly is common. I haven't used EAs story progression in years but I know it isn't perfect. If you're already using mods and may consider one day using story progression... I reccomend grabbing the NRaas: Story Progression instead. The SP mod along with other NRaas mods have adjustable settings. All it takes is a little reading and if you need further help, you can post in the NRaas forums. Most of the mods have a FAQ page along with the Interactions page. The Interactions page listing every setting and of course, the FAQ page listing frequently asked questions.

NRaas: Story Progression Rotational Caste Settings suggestions for those who play householdsin a rotation

@nickibitsward Just as Zei says... NRaas: Overwatch can be used to disable the neighborhood pet adoption system.
click on a computer or city hall for mod menu | NRaas > Overwatch > Settings > Stop Pet Adoption
NRaas: Register can be used to disable strays. (Deer, Raccoons, Cats, Dogs, Unicorns, & Wild Horses).
click on a computer or city hall for mod menu | NRaas > Register > Animal Control

I think those are the right steps... can't check atm.