I don't believe that BART was designed for 100,000/week number. I read that it carried that many riders *when it opened*, but there's no way anyone would design a grade-separated rail system for 100,000/week. That's not even a notable amount of riders for a single bus line.
Design capacity comes down to track layout, train capacity, headways and station design. The trains and stations are not particularly crowded by world standards. There is a bottleneck in the system (the transbay tube) that several different routes use, which limits headways. But honestly the system is doing pretty well serving 400,000/day.
The real issues are the electrical system, old rolling stock, and lack of maintenance. Not design capacity.