And I just don't find this surprising at all. And I've seen this on more older machines than not. I feel that the manufacturers never anticipated constant data throughput over 300 baud. At the time (1979) a 300 baud modem was high end and quite expensive. A lot of stuff was 110. I also know that by the time of the model 16(a) these ports definitely supported hardware handshaking because we used them with 2400 baud modems and dialin users under Xenix.It further surprises me that the serial ports behave like this, yet they use standard Z80 SIO chips. One might expect that, if Tandy had chosen some odd combination of TTL, line drivers and other stuff to implement the ports, that you'd see these anomalies, but surely with a standard implementation, the interface's behaviour should likewise be standard.
I think the real problem is that hardware handshaking can be made to work, it just doesn't with the programs you are currently trying to use.