A simple google search before posting would have made your fictitious scenario a little bit more believable.
Technically true but it is often paired with loratadine in, e.g., Claritin-D. Many allergy sufferers also get congested sinuses.
The side affects of prolonged pseudoephedrine use (usually defined as more than 7 days, btw) are far more serious than a stuffy nose.
You cannot even purchase enough pseudoephedrine to use every day over a full month. The government restricts maximum grammage per month - and no doctor is going to prescribe long-term use of pseudoephedrine to "help with allergies".
That is to say I don't believe your story at all. But I get it - googling these things before you posted would have "cost" you approximately $24 or something something something...
If one can treat the symptoms just as easily as the cause and pseudoephedrine doesn't make them feel like a drugged-out zombie, just guess which drug people are going to take...
...and yes, doctors actually will write prescriptions for pseudoephidrine because they're generally pretty sure their patients aren't using it to make meth. I know three people who've gotten such prescriptions, and I've been tempted to do the same thing myself.