Feld Entertainment was the biggest operator of these kind of "family entertainment" stadium/arena shows. They still have Monster Jam and AMA Supercross, but I'm thinking their bread and butter right now is Disney on Ice. And they still own Ringling Bros although that's being revamped as previously noted. On top of that they produce Sesame Street Live and Marvel Universe Live.
https://www.feldentertainment.com/productions/
Feld is a powerhouse, and probably produced some of the circus performances the OP remembers, as they bought out RBBB in 1967. They had to do furloughs during the worst of the pandemic, but were the first touring productions to go back on the road, and have now rehired most of their Ellenton production staff and are hiring performers at a fast clip to ramp up the international tours now that going abroad is possible again. I know several skaters who have worked with Feld as performers. (Also, of the list of touring children's shows the OP mentioned, Feld produced all of them except the
The Wiggles and
Raffi. They also produced the
Ice Capades and
Holiday on Ice after 1979.)
Part of the issue in rural areas is the decline of rail transit. It used to be that shows traveled by rail and could stop at just about any town of any size that was on the line without incurring much extra cost, but that's not the case with a truck fleet that uses arena buildings for stages instead of tents carried along with the show. The minute you leave the interstate highway system, costs begin to climb because of the slowdown in travel speed, and in rural areas it is often difficult to find arenas with enough seating (and enough power capacity to support theatrical sound and lighting) to enable making a profit. It has always been the case that the only way remote areas get professional traveling entertainment is when it is easy and profitable to stop en route to somewhere that could support a run of several weeks. Cinema killed Vaudeville, and streaming TV is doing its best to kill movie theaters.
That said, local non-profit family entertainment is all over the place wherever communities, schools, and/or houses of worship have chosen to make facilities available for it. You pretty much have to grow it at home (with perhaps a few hired professionals added to the group for wow factor), but when it comes to kids' shows, the audience tends to be very happy with dedicated amateur talent. Most public libraries have storytime programs, and if they don't, perhaps local support for added funding can help make it possible. I help stage a 4-show nonprofit suburban production of
Nutcracker on Ice every year at a public rink, and we have hundreds of repeat audience members who have no connection to the young performers, but who would not dream of missing it. I grew up in the rural South. When I was in grade school the school district brought in high-school kids from surrounding counties to do shows for us, and when we were in high school they brought in college theatre groups from elsewhere in the state who were happy to do on-the-road productions at our high school and make a bit of money for their program. We had a lot of local folk festivals as well (some fairs with traveling carnival rides, but more festivals with amateur performances and contests like cookoffs.)