Biden and Trump spent equal amount of time on vacation. This means that if you contend that Biden spent all 4 years on vacation, then you have concede that Trump did the same.
The difference is that Biden spent most of it at home in Delaware or Camp David.
Trump spent most of it at his own properties, and charged the tax payers for lodging for his staff and the secret service.
Now if you want to stick to your own question, then the answer should be no, the President should not be paying for his vacations. it's one of the perks of the job and should remain that way.
