hello; Can you run a tank without some sort of bubbler? Yes, I have done so. However I only tried running tanks without some sort of a bubbler for a decade or so. The other four decades or so I have used them including the last two.
The absolute best thing I can say for air pumps and bubblers is they have saved my tanks many times. In the late 1950's and 1960's air operated equipment was all I had. Had air operated HOB filters as well as simple bubblers.
Somewhere along the line, say the 70's, power filters started being available. They were not reliable. Several times a week they would lose siphon and all that was operating would be the air pump.
Eventually the power filter designs got better to the point they can be relied on for the most part. I still do find a malfunction from time to time but they are more rare. I now run power filters on most tanks and some sort of bubblers together.
I get that many do not care for the history of things and may tend to dismiss the above as old school. Let me point out that what worked in the past will work now. With an air pump and a few sponge filters I can keep tanks going when the other stuff fails. You can even get battery operated air pumps for when the power is out.
I keep some sponge bases in my power filters to keep them loaded with bb and can set up a new tank quickly with them.