The limited performance of the low-power microcontroller isn't the only problem. The R/F signal itself is modulated at a low baud rate. If it's modulated at 1 Mbaud then each bit is sent as an R/F symbol that's 300 meters long in the air. In a sense the R/F receiver needs to demodulate "300 meters of R/F analog data" to be able to decode it to a 0 or a 1. If there is a little delay or noise at the beginning of the 300 meters of data because the signal is being relayed (if you can visualize what I mean), then the receiver isn't going to notice.
The low-power constraint on the keyfob (as it's powered by a small battery that must last years) prevents manufacturers from developing R/F physical layers and chips that are performant enough for precise distance-bounding.
The most practical one, I think, is to make it NFC-near instead of BLE-near. Or, you know, just use a non-contactless one. Or add a button.