My cat Loki has been sleeping with me near or on my pillow since he was a kitten. Now that we have the room air conditioner on for the summer months, he seems to favor his spots in other rooms...but is welcome and will likely return when we retire the AC for the winter. He sleeps with us also when we go camping in our camper.
My dog always had a dedicated spot at the foot of the bed on my side (king sized bed), but he's older now and suffering with some health issues including arthritis, so he no longer joins us, but sleeps on the carpeted floor at the foot of the bed. Our last girl dog had severe epilepsy, among other health problems, and she slept between our pillows. That was good for us, as when she had seizures in the middle of the night, we were well aware and could assist her.
We never had any kind of flea issues where I live, and that's all I could think of that would mandate me to take care of the problem before inviting the pet onto the furniture. My pets have always had full access to the home, as they are part of the family and no less. I never had pets other than fish, etc. as a child, so now I welcome them everywhere I go as my furkids.