First to reply to your question, when you befriend the innkeeper you get to use the inn bed for free until you pay for it which restores it to its proper cost/day. Besides this bug, the prices are unaffected.

To the issue at hand: If players feel the prices are wrong they can suggest different values along with their reasoning. In my opinion the current values are as fine as fixed prices can be. Adding sliders to affect such minor issues would make the MCM look like a MIDI console.

Furthermore, the real problem is the fixed prices themselves. Innkeepers and coachmen would charge little to poor people (why lose a customer?), more to rich ones, much less to friends and provide discounts to those who could convince them.

For example:

Basic price: 50*SQRT(level) for inns, 60*SQRT(level) for carts + special modifiers (eg. travel to Markarth should cost double)
Friend: -50% discount
Basic speech perk: -10% discount
Merchant speech perk: -10% discount
Silvery tongue perk: -50% discount for opposite sex (women get affirmative action here)

On the contrary: prices should drop for experienced characters. The carriage driver should be pleased that a seasoned warrior is traveling on the cart: less problems with highway man and other low-life .

And an innkeeper might the use the fact that a well-known person decides to stay in his tavern as an advertisement factor and thus also charge relatively low prices.