Why is it impolite?
Just copying my comment to Jacob Davis's answer in case the post, or my comment is deleted.
You don't say this to someone you're asking a favour of. One should aim to be grateful (presumably the person will do the favour), humble (you are the one asking, the professor has no obligation) and appreciative (you acknowledge that the professor is busy) at the same time.
It's all about tone, and if the English language had a formal version of ‘you’ today, the professor would have been less peeved. Let's pretend thou is formal—originally it wasn't—how would the sentence sound today?
"I would appreciate if thou could reply as soon as possible"
Unfortunately, thou is practically obsolete in contemporary English, and many speakers of Romance languages, and non, find themselves in the same predicament as the OP. How to be extra polite and show respect to someone using you.
Modals, and Thank you’s
The expression, ‘I would appreciate’ is super polite; and using another modal like could is highly recommended. In fact, the OP wrote ‘if you could reply as soon as possible’, again super polite, I can't fault it. But when you're asking a favour from someone who has authority, it might be considered "brash" to ask them to respond ASAP, even if you soften it with all the ‘woulds’ , ‘coulds’ and ‘mays’ in the world.
If you're British, first of all you apologize: ‘I'm sorry to bother you’, and then you use a conditional tense: ‘I was wondering if you wouldn't mind sending my transcript, I would be extremely grateful if you did.’ You would explain why you need it, and then conclude your email with, ‘Thank you for your time.’