Indeed, but how does a Driver know what that set speed is, other than by experience (of them and others)! It is surely possible, on a dry day with a good set and a confident Driver, to exceed the OSS setting while still being at or below the PSR speed at its start.
Although there were the occasional trip reported at PSR TPWS installations, the vast majority of TPWS trips that were reported in my area when I was S&T team leader were for TPWS OSS or OSS+ installations associated with TPWS fitted signals.
There were also a couple of buffer stop TPWS trips reported.
As I'm not a train driver, so I can't really give much advice other than to repeat that as TPWS is a compromise, drivers should consider what braking and speed reduction would be required for stock with the older type of braking system. That's what I meant by driving more cautiously. If you reduce your speed to give a greater margin of distance before the commencement board / before the signal at red / before the buffer stop, that will be more similar to the braking curve of older stock. Hence there is a much reduced chance of tripping the TPWS.
As many drivers have found, when driving a modern train (with a really good braking system) in dry conditions, they can brake later and still comply with the PSR / stop at the signal / stop short of the buffer stop. But get caught out by unintentionally tripping the TPWS.
Alas because of the design of TPWS, there is no straightforward technical fix to this problem. TPWS is fundamentally a "dumb" system (it's not computer based) in that it cannot differentiate between a loco and MK2 stock and a modern EMU/DMU etc. that has modern high performance brakes.
As a comparison, ATP and ERTMS/ETCS are computer based and the trains onboard computer can constantly recalculate the wanted braking curve vs. the current speed and braking performance.