Suppose for a second that the pet adoption segments never existed on the show, and was something that the new regime (Mike and Drew) had brought in.
Wouldn't it be something that we would be complaining about, since there is no logical connection between animals and the show? Isn't this more of a "variety" show item than a "game show" item?
I think the problem with the new regime is that they can't properly present anything. A good presentation needs to be short, involve interaction, and have a purpose. Something like the pet adoption segment with Bob was for a good cause, and it was short enough to not completely take away from the track of the show.
I wouldn't have minded those house bands like Dollyrots and Lonestar if Drew had actually interacted with them and/or there was a purpose for them on the show. Instead, Drew would just go crazy and repeatedly yell "It's the Dollyrots! It's the Dollyrots!" and give zero explanation as to who they even are or why they are there on the show. I also wouldn't have minded that breast cancer awareness recognition if they did a quick spot of it, and move on. Instead, we get a whole special, with Drew reminding us every 5 minutes with something along the lines of "Hey, it's Breast Cancer Awareness Month!" Reminding people to the point of nausea is not going to make people more interested in the cause; if anything, it's going to make more people switch the channel.
So, would we have complained about it? If it was done like it was during the Bob era, we would've welcomed it. But, if it would be anything like the above two examples, you're damn right we would complain about it. And I bet if we get some kind of pet adoption special in the future, we're gonna hear complaints about that as well.