The present TRRA members are UP, BNSF, NS, CSX, and Canadian National (through their acquisition of the Illinois Central.) The shares aren't equal and are roughly proportional to who bought how many owners from when the TRRA membership was at its largest. (By the middle of the century there were a more than a dozen if I recall correctly: MoP, NYC's Big Four [CCC&StL], Pennsy, Wabash, NYC&StL, IC, B&O, L&N, GM&O, Frisco, MKT, CB&Q, and C&NW. There might have been one or two others I'm overlooking, and some owners had already been swallowed up by mergers even then, but it was basically the railroads serving St. Louis mid century minus IT.) KCS could possibly join, but their entry into the St. Louis market is pretty recent, and by way of acquiring trackage sold and resold a bunch of times where other railroads kept the voting rights. UP is the largest shareholder with the other folks being about equal. (Per Wikipedia exactly equal, but I'm not sure that's correct. Haven't checked the corporate structure lately. They say UP has three shares and everyone else one. That approximately jives with my memory, but I'm not a TRRA employee or a TRRA Historical and Technical Soc. member, so don't quote me on that.)
Anyway, my recollection from railroad connections is that the restriction is to one train at a time rather than one way running. It's been one train at a time for a good twenty years now, I think, though it's only recently that they've taken the south track out of service entirely. (And indeed demolished much of the western approach structure.) Given how much they've thinned out the rest of the system I'm not sure how much of a bottleneck three tracks across the river really presents. Some, probably. Especially when they're working on the MacArthur. (As they have been recently.) But maybe not terminally. (Hah. I kill me.)
All that said, yeah, it probably needs replacing. I'll be darned sad to see it go. I'm really quite fond of that bridge. But I don't see it as one that's likely to garner a lot of excitement for repurposing, and I doubt there's any good way to really stabilize it enough for continued railroad use. Honestly, even the MacArthur is probably nearing the end of its life expectancy, which might be why TRRA is so eager to get one replaced now. Make it less of a headache twenty or thirty years down the line.