Just how long does the shielding have to withstand high temps? We already solve a much harder problem with reentry of orbital vehicles. The problem here is much simpler, as we don't actually want to shed most of the velocity. In fact, we want to lose as little of our kinetic energy as possible. If ablative shielding can handle reentry, it can handle launch. AFAIK, the mass ratio for reentry shielding is quite good.

The rail gun cargo is going in the opposite direction - you start in the thick air at a speed greater than orbital velocity. It's been years since I could grind through the numbers, but it makes a big difference

This speaks to my point. In launch accelerator mode, you want to dissipate as little energy as possible. In reentry mode, you want to dump the majority of a big honking chunk of kinetic energy.

I'm sure there are all sorts of optimizations to consider. How about a mostly vertical trajectory, with most of the horizontal velocity provided by lasers heating a heat-exchanger?

By keeping the trajectory mostly vertical, one can avoid most of the lower atmosphere by stationing the opening to the atmosphere miles above the surface. This also limits the downrange danger-zone for falling malfunctioning cargo pods. Additionally, it makes the cargo pods easier to target with the lasers, since the powered flight would be entirely in the upper atmosphere. It would also make the rocket nozzles easier to design.