Currently, miners earn income in two ways, one is fees and the other is mining new Bitcoins. When Bitcoin cannot be mined, maybe many people may stop mining and maybe we may suffer for this, I thought. That's unlikely to happen, because Bitcoin is designed to be able to accept money in all situations. The Lightning Network is currently being used for transactions, and a larger alternative may emerge in the future. At that time, we may have to pay higher fees, but that may not be the case.
You said my mind in the last part of your post which is that we may likely have to pay higher fees when the total of 21 million bitcoins have been successfully mined and bitcoin mining completely closed.
At this time, the only means through which miners will be making money is through confirming bitcoin transactions on the bitcoin network, if fees does not increase, lots of miners then may find confirming bitcoin transactions unprofitable and may shutdown their system, so to keep the miners online to continue to support and protect the bitcoin network, they have to be earning enough from transaction fees..
And the unfortunate thing is that 99.9 percent of us who are here today maynot be alive to witness what will happen to bitcoin when the entire 21 million bitcoin gets mined, thir is a harsh reality but death is a call every body must answer one day.