I've never heard of anyone doing this, never seen anyone do this and I've been gardening since I was a wee child in the 1960s. It simply isn't necessary. The flower falls off on its own at the right time, and I suspect the plants do not appreciate human intervention. I don't know if there are any negative side effects from you removing the flowers too soon, but suspect that it might interfere a tiny bit in proper fruit development since the tomato plants function perfectly fine if we just leave them alone.

I've never heard of deformed fruit resulting from flowers staying on the plants too long. You get deformed fruit because of certain weather conditions that are occurring when pollination/fertilization of the flowers is occurring. Once the weather straightens out, the deformed fruit will stop. The most common kind of tomato fruit deformity is called catfacing and it generally occurs because the fruit set at colder temperatures than they like. Sometimes, in very warm weather, catfacing can occur due to pollen issues caused by high temperatures at or above 92 degrees occurring while pollination is ocurring, but I rarely see that sort of heat-induced catfacing. I do see the cold weather-induced catfacing on early tomatoes. It also can happen during times of high humidity when the high RH values make the tomato pollen sticky so that it clumps together and does not move around well inside the flower, which is where pollination and fertilization occur. It is what is is, and it stops when the temperatures stabilize.

Catfacing is addressed in this factsheet from OSU (though I don't really like that they list is as a noninfectious disease---to me it is more of a physiological issue than a disease).

Tomato Fact Sheet From OSU

I'd leave the flowers alone and let them fall off the plants on their own simply because what you're doing is not helping the fruit and might be hurting them.

The reason I think it is causing the deformities is because I've noticed that when I removed some of the flowers that appeared to be stuck, the part of the tomato where it was stuck to has been deformed. Maybe it's sticking because it is deformed, and not the other way around. Who knows. Thanks for your response, Dawn.

You're welcome. The flowers probably are sticking due to moisture or high humidity, and the tomato was fated to be deformed before you ever see it appear as a tomato. We cannot really prevent catfacing, especially here in OK, where the temperature fluctuations are crazy at times. Some people remove small tomatoes with lots of obvious catfacing because they know from experience that sometimes so much of the tomato is lumpy, bumpy and malformed that there won't be much of it that is usable once they cut into it. Their thinking is to ditch the malformed fruit so the plant will put its energy into producing more fruit that might be more normal. I usually just leave the fruit and take my chances that they'll be usable, but I have a lot of space and a lot of plants. Some varieties (especially open-pollinated, large-fruited types) are more prone to catfacing than others, so if you grow those varieties, you might want to try something else. It just so happens that I think some of the varieties most prone to catfacing are also some of the best-flavored varieties that I adore, so I grow them anyhow.