The obligatory can’t-get-a-straight-answer-on-the-Dope-answer: It depends.
If we’re talking about tea tea that I’m drinking as a beverage, then usually not, 'cause I don’t want the bitter flavor. If it’s for a belly ache or topical use to bring down swelling, I want the extra tannins that come out when I strangle the teabag.
Herbal “teas” (really, infusions, but everyone calls them teas and I stopped fighting that fight years ago) depend on the herb and what chemical constituents I want in the cup. Bitter alkaloids and tannins tend to wait until a long steep or a squeeze to extract, so if I want those properties, I squeeze. If the medicine is supposed to taste like crap, squeeze it. If it’s supposed to be pleasant tasting and mild, don’t squeeze it.
(This is true even when I use a teaball or loose tea in a strainer.)
My cuppas are made with loose tea in a strainer. No strangling or squeezing.
When I make iced tea (Arnold Palmer in a pitcher, lately), my obsession with precise measurements comes out and I am compelled to get as much of the liquid that is trying to escape in the tea bags out by smooshing them up against the side of the pitcher. If I were making straight iced tea, this would be less of a thing as it wouldn’t be like I could screw up the ratio.