Disclaimer... The following is just one opinion, but it does come from some first hand experience with this and other routes.
On the other hand, the southern states currently seem to have the least restrictions, and be the most advanced in opening up. So maybe the Southern Tier would have fewer obstacles and more choices for food and accommodations.
That may be a factor, not sure how true that would be. Factoring in that the ST has sparser services to start with I have my doubts, but I really don't know what things are like on the road during these pandemic times on any of the routes.
I am of the belief that, with proper precautions, heat is no obstacle. I'm sure not everybody agrees with me, but my perspective comes from living and exercising in Phoenix for 20 years. The residents of Phoenix do not crawl into a hole in the summer. They continue to run and bike and play outdoor sports, even in the middle of the day. The trick is water. Just make sure you drink gallons of water, and know your body. Know how to recognize the signs of heat stress and heat stroke.
I have a few problems with that. Doing all that stuff when at home where water is easy to have available and AC is nearby is one thing. Doing it on tour is another. Doing it on tour on a route that has any services extremely widely spaced is still another. I recall some very long stretches on the ST with no chance to resupply water, no chance to pop in to air conditioning, and even no shade. On a mid-Feb thru mid-Mar trip I needed to carry a lot of water at times. If it were to be 110F I can't imagine how much water I'd have gone through or how unpleasant it would have been.
These days, I live in Tallahassee where it is summer 9 months of the year so I have put up with a hot summer day or two. I remember a few days in the SW like a few where we were in the Needles where the heat was relentless or one near the aptly named Caliente where I was rationing my water in triple digit heat after finding no water available where I thought it was. I have voluntarily gone out and trail run in 95-100+F heat quite a few times. Doing that and being stuck out in the heat in the emptiness of much of the ST are two entirely different things. Water stops and other services are just too widely spaced for it to make any sense to subject yourself to it in my personal opinion. It isn't like you usually have the option of riding for a few hours in the morning and then sitting in the shade or the AC. I guess you could ride at night, but many (most) of the places I camped wouldn't have been that great to have slept or hung out in during the day in the summer heat.
John, I have a lot of respect for your opinions in general. In this case I do wonder about whether this particular one is based on any first hand experience with this route or one with similarly long hot empty stretches in summer. If so my hat is off to your toughness with regard to your ability to survive and thrive in the heat on tour in remote country. I'll be the first to concede that I have not ridden it in summer, but based on having ridden the route in late winter and having done other riding and hiking in the area I know that personally would never even consider it in Summer. Having been caught in an early heat wave in the spring in the Sierras and record heat on northern routes were tough enough for me. We had record heat for much of our Trans America, but the resupply points are much closer together as are the places to find shade (even there sometimes a shade tree or a cold bottle of water felt like a rare pleasure). It should be noted that the ACA doesn't recommend it for summer either. They even caution about the possibility of extreme heat in September and May.
The thing is for me the ST doesn't really offer all that much compared to the other possible options. Doing it in summer you'd be suffering with hauling huge amounts of water between widely spaced resupply point, past monotonous scenery, through brutal heat. In exchange you'd get the shortest XC route with the least climbing and an interesting sampling of people and cuisines. So IMO, much better to just do a more northern route unless you must do choose it for the shorter duration or really want the reduction in the amount of mountains. In that case I'd do it in cooler weather.
Brutal heat is something that sometimes you can't avoid in the US in Summer for a coast to coast trip, but when there is a better options I really don't see subjecting myself to the worst one. Then again the ST may be someone else's dream trip for reason's that I just fail to see. Someone else may love the solitude of days and days of empty brown sagebrush.