I have also been working in this field for last few years. We do not have any analytic theory to solve "gravitational N-body probelm" so the use
of supercomputers seems to be ultimate choice.
There are many drawbacks of this approch. Computers work like "black box", we do not know what "actually happens" when a system evolve.
Everbody use his or her own "codes" and "machnines" for simulation and there is no standerization so there is little hope to compare results of one simulation to another.
Last but not lest in place of trying to understand physics, most of the time people just compete for bigger and bigger simulation and it cause wastage of governments money.

How will the understanding of Physics help solve the problem...?

The main aim of science is not just to know the
answers, it also want to know, how the answer was
obtained. My point is that, in order to solve scientific problems we should follow that approach, which can ge used for other problems also.

I don't think that the N-body problem exactly qualifies as a black-box type problem, but I think I understand your argument. For some problems, particularly certain types of complex adaptive systems, I can't imagine a better approach than simulation - that is, I can't imagine an analytic solution to the problem.

Computer time is now cheap and so it's easier and vastly less expensive to solve certain problems numerically than to attempt analytic solution. My perception is that in the 60s and 70s the Russians were doing much better at developing math than the US mainly because they didn't have computing resources and they had no choice other than to get smarter.

I think it's a situation with perceived cost-benefit. People think, "Why spend all these resources when we can just do it numerically?" OTOH, it would be good for N-body even if we had a proof, say, that there is no analytic solution. That way we'd know up front if it were a waste of time.

Somehow I think we're going to be waiting for the next Newton, Gauss, or Erdos for an analytic solution to N-body. In the mean time there's all these underutilized computing resources lying about.