Hey @RasHam, hope you are good.
Transaction fees does not increase over time, it adjust based on the amount of participants that also want to mine a transaction, the more participants, the more transactions could increase, remember bitcoin have a limit on the amount of data that can be appended into a block, 1 to 2mb.
Just for example: lets say each block is capable to store 1000 transactions, minimum price fee per transaction is 1000 satoshis per transaction (those 1000 satoshis is to pay a miner to mine your transaction, they are the only one with the ability to append data into the blockchain).
Now what could happen if there is a constant increase of 1000 transaction each 5 minutes?
Blocks can be mined 1 every 10 minutes, so users start competing each other for the powerhash necessary to mine a transaction, and they are willing to pay more then the normal price fee for a transaction, lets say 1200 satoshis 1 user… miners always take first the transactions with the higher fee possible, so all the rest of the transactions will remain in the mempool, while people compete to get their transaction mined in the next block (10 minutes).
Now the price will just adjust at the end of it, people would not pay way too high fees for a tx, they could wait until price goes down, and it will, because there will be a moment when the mempool runs out of exceeded amount of transactions.
Here are some links to go in-deep with this subject:
If you have any more questions, please let us know so we can help you!