> The shuttle program was ended because there's no way to make the ceramic tiles safe.
Well... You could go the Buran route and put the engines on the booster. Then you could put the shuttle on the top of the booster and keep it safe from falling foam, with the added benefit of having some extra cargo space.
The VAB would have to go through some refurbishing.
There's a lot of great technology from the Shuttle, such as the avionics and the engines, that could be worth reusing. A lot of research work was done on Shuttle derivatives in the 1980's, but nobody was interested in making the investment to retrofit the VAB and the launchpad.
That, of course, is one of the great challenges of making improved launch vehicles. You ~might~ be able to lower the operations cost by investing in research and a new design, but the cost of the research is guaranteed to be high.
Falling foam is the threat to the tiles that everyone is thinking of (because it's happened), but it's not the only thing that can damage them. The tiles also have the big problem that they're expensive to maintain.
There are many alternative concepts for heat protection for re-entry, but there's no interest in making expensive research investments in something that could fail. Manned spaceflight is going back to 60's era ablators because we know they work.
To be sincere, the idea of sending a 737-sized reusable spacecraft to LEO when it usually lands empty is not practical.
You could send the the payload up on non-reusable vehicles and, after a couple trips, send a reentry vehicle to bring down anything that still can be reused.
Actually, if you restrict yourself to a hypothetical "need to build something Shuttle like using available technology" universe then you can get something safer fairly easily. Buran, for example, was considerably safer for a few reasons, but we could make something even safer.
First, ditch the SRBs, they are a severe safety hazard (they led to one Shuttle disaster, for example) because they are segmented, they can't be throttled, they can't be turned off, etc. That leaves you with a thrust problem though, due to the low thrust of LOX/LH2 engines. So, second, replace LOX/LH2 with LOX/Kerosene. Now you have plenty of thrust, now you don't have to deal with super-cryogenic fluids, now you don't have to eke out every possible mass ratio boost on the ET because both LOX and Kerosene are fairly dense. Now you can ditch the foam insulation, and ice formation is slightly less of a problem.
Third, take the engines off the orbiter and put them on the booster (ET). Now you've created a vehicle, like Energia, which you can launch non-Orbiter cargo with. Realistically you haven't made things more expensive by throwing away expensive high performance engines every trip because it takes so long to inspect, refurbish, and re-install the SSMEs on the orbiter anyway that it's a wash money-wise, and probably for the best time-wise. On the plus side now the orbiter doesn't have to support the thrust of giant engines so its frame can be made lighter. Also, it doesn't have to bring those engines back down to Earth, so it can be yet lighter again.
Fourth, snip the wings off the orbiter. Turns out the military didn't really need a several hundred mile cross-range landing flight capability on the orbiter because the super-hypothetical mission that was designed for never turned out to be even remotely practical. So, smaller wings mean less mass and, again, a lighter frame. Now you've reduced the orbiter mass by a crap-ton and gotten rid of the huge amount of super vulnerable leading-edges on the wings. Now you can use a less sophisticated thermal shielding system on the orbiter (since it's lighter, smaller, and barely has wings at all), you don't need the carbon-carbon composite wing leading-edge bits, you don't need the vulnerable ceramic tiles that need to be meticulously inspected after every flight.
Now you have a vehicle that is much simpler and safer and yet does essentially everything that the old Shuttle system actually did in practice.
Granted, if you were designing something from a clean sheet at this point you would never end up with anything even remotely resembling the Shuttle.
Well... You could go the Buran route and put the engines on the booster. Then you could put the shuttle on the top of the booster and keep it safe from falling foam, with the added benefit of having some extra cargo space.
The VAB would have to go through some refurbishing.