> I understand the meanings of the flags but my question
> still remains.  Can you give an example where
> testing TRMT allows you to do something that just
> testing TXIF exclusively couldn't do?

In addition to the examples put forward by Dave Tweed and
Martin Buehler, there is the time delay. Loading TXREG with
data takes a small number of cycles. One cycle to move TXREG
to TSR. But the data could take hundreds of microseconds to
transmit. A 9600 baud byte is around a millisecond for example

> You can poll TXIF without using interrupts.

Of course. I'm not saying anything is compulsory, just that testing
one or the other may be efficient/necessary/elegant in some
situations. The UART itself is fairly simple, but you could write any
number of software structures to use it and so many variables it
would be easy to concoct an example

> Also, I can't see how knowing that the data is sent out (TRMT=1)
> helps.

The obvious answer is that in some cases you can then direct the
s/w or h/w to then move on to doing something else

> It certainly doesn't tell you that the data was received at the other end

No, it doesn't. Verification would be a whole new ball game, but
doesn't necessarily alter the way that the UART is used

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