The thing to remember is nothing is black or white but various shades of grey. If the signal has ionospheric propagation then the polarisation gets mixed and so there’s not normally any polarisation benefit to being the same RX polarisation and TX.
I don’t recall seeing too many “amazing” 2m polarisation events in my 35.5 years on hamming. But I do see more as you go up in frequency. There’s the 23cm event Stuart mentions and I offer this 70cm event from my past: Loss due to polarisation error - #7 by GM4LLD and this 23cm event from Andrew G4VFL’s past: Loss due to polarisation error - #9 by G4VFL
And in all 3 people were on summits so relatively clear of nearby reflecting surfaces, e.g. house roofs, only the ground to affect things. Normally, in the UK at least, when there were many hams with VHF and up beams, most were mounted on a pole on the chimney rather than masts due to our twee gardens and houses. If you were lucky your beams were 10m AGL or about 5 wavelengths for 2m. 70cm antennas would be 15 wavelengths clear and 23cm 45 wavelengths clear. Professional RF dudes will tell you getting beam antennas 45 wavelengths clear of the ground gives them a warm gooey pleasant feeling. 
Tropo scatter doesn’t seem to affect the polarisation much… there are reasons why horizontal is preferred for VHF and up DXers but if there was significant polarisation change we would need mixed polarity receive antennas and they’re not found commonly. So enough horizontal tropo scattered signal must arrive for horizontal transmission for it to be viable.
Likewise, diffraction doesn’t seem to affect polarisation. I’ve worked plenty of people VHF handy to VHF handy when there have been serious sharp ridges for the signal to diffract over.
The major source of polarisation change seems to be reflection of ground based objects.
Do you need H and V polarity? No, things will work. But if you can switch or run both then things will be better.