Market actors are allowed to charge whatever they want. Price controls are super bad. It's not the role of the state to mandate a specific price. It is the role of the state to make sure prices are fair and transparent. Deception cannot be tolerated in an efficient market.
No, the reason they tack on the fee as a "tax" is literally to confuse and otherwise mislead the public to the true cost of the product they're buying, or mislead where the money is directed. they're buying from. If you believe in the Tennant's of capitalism at all, then you must have clear price representation.
Isn't Airbnb a good example of this? In some locations you have to open each listing to get the true price and it's a huge waste of time. In locations, what you see on the map is the real value, cleaning and other, fees included.
I wish sales taxes would be added - some cities charge very large taxes on hotel rooms and so it might be worth staying in a hotel not far away with more reasonable taxes.
And that comparison is important - when junk fees are allowed more honest companies suffer because consumers might shop around and end up choosing the option that is actually more expensive. Those consumers might be on page 12/13 of a form and just accept the fee to avoid the hassle - or they may assume everyone (including what looked like a more expensive competitor) is baking the fees in late in the process and not bother investigating deeper.