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Yes, tapeworms usually don't show up on a fecal float. That isn't what the vet is looking for when you bring your cat and a stool sample in and tell them you've seen tapeworm segments. The vet wants to check the stool to see if there are any other kinds of worms because an animal that has tapeworms obviously has some exposure and could well have other types of worms as well. The vet has a few choices for medications to treat tapes, but one option will only get tapeworms while other options will get tapes and other worms too. It just makes more sense to test the stool so that you only have to give one dewormer if possible. It's less stressful for the cat, the owner who has to give the medication, and you get more for your money if you can use one medication and kill multiple types of worms rather than use one medication for tapes and then have to go back and use another one later.
As for the form of the medication, the vet I work for generally uses pills. Personally I prefer pills for most cats as I can be sure I got the entire dose in (or not) rather than liquids where an unknown amount is spit out all over me and everything near by. But for the cats that just can't be pilled, we do use an injection to kill the tapeworms.
As to the requirement of an exam and prescription, some of that may be a legal issue. The way the law is written in my state there must be an established doctor-client/patient relationship. So legally we can't dispense medication or prescription food of any kind unless we've actually seen the animal. You can thank malpractice lawsuits for that one, I'm sure.
