Is having only 1 credit card, crazy or logical?

TL;DR: Think about your spending habits first and see what fits.

You are free to have however many credit cards you wish as long as they're approved. The banks should be checking your income. There are also credit cards specifically for students, so those should not be checking your income.

If you want to cancel a credit card, just stop using it first and pay off the debt before cancelling.

The pros of having multiple cards are that each card has its own niche in terms of promos. E.g. dining card, groceries card, online shopping card etc.

However, that also means your expenses are split up, so it's more difficult to hit any minimum spending sum stipulated by each of the cards. If the cards are from the same bank, perhaps the sum can be shared across them.

It also means your bill cycles can be all over the place (the cycle is based on card activation date or something like that) if you apply for credit cards at different times. But, it's doable to adjust it (For one of my credit cards, I will need to go down to the branch to do it. Not sure if that applies to all banks) if really needed.

The pros of having one card are that you have only one source of card bills to worry about. In exchange, you will want to look for a card that can fit your spending habits snugly if you really want to maximise those cashback/mileage/points etc.