Right now, cartridge memory (CM) in an LTO tape is 16 KB. That's how much you need. The tape will read the full inventory in the header on load, which takes only a second or two, and quickly space to the proper point along the tape.
If anything, increasing the capacity of CM to 1 MB would be possible and would solve some 50% of problems with low capacity of the CM (although would introduce another one -- it takes bloody ages to read that CM chip due to low throughputs involved). NFC with Bluetooth could probably solve that throughput problem, at the expense of power required. Adding a second chip for redundancy wouldn't hurt, either. Cost would go up, and that might not be appreciated.
As I see it, though, there's just no need for extra connected memory. If you want to index the tape contents, do it at the host level. That way, you're making the index easily accessible to all applications, you can quickly rebuild the last known good index to tape without having to re-read most of it and you don't have to rely on a mechanical connector that's prone to breaking.
Okay, reductio ad absurdum:
If adding a small amount of memory makes sense, adding more would make even more sense. Why not go the whole hog and replace tape in the cartridge with flash memory, then?
Food for thought: You could fit thousands of micro SD cards in a single 4×5×1 tape cartridge (or hundreds of USB sticks, etc.). Then add a beefy connector at the front (like aggregated 8 USB 3.1 ports) and off you go. With USB 3, you could get away with using the slowest sticks in the "cartridge", have 8×USB 3.1 hubs and putting all sticks in it in a RAID.
I wonder if there's someone making all the decisions, reading this and deciding: Hey, that's actually a good idea, we'll build it.