If your tractor puts out the recommended flow and psi, then there is one thing an independent pump can do, albeit with risks. - It can reduce the engine speed required to operate the hoe. This may save you fuel costs.
The hoe has a preset pressure limit. No matter what the rated pump pressure, the relief valves will operate at the same pressure, so you will not get more digging force no matter what pump you use. Change relief setting (your risk) , change cylinder size (your risk) and you can increase force, change pump you can't.
However pump output is proportional to engine speed. If your tractor pump puts out 10gpm (at PTO speed) and you install a 20gpm pto pump, you can run the engine at half rated speed for the same flow.
BUT!
You risk lugging the engine when you load down the hoe at half PTO speed.
AND
You have no mechanism to prevent running at PTO speed and feeding 20gpm to a hoe that's only sized for 10gpm.
AND
You could size the pump beyond your PTO HP, and lug the engine even at PTO speed!
Plus you now have a second pump, second (and larger) resevoir etc. to maintain. Buying a 12 GPM pump (versus 10) and running it at 80% speed would probably be low risk, but is it really worth it for the minor fuel savings? Even running at PTO speed is probably low risk, with slightly faster movement, but do you need more speed or force?
I'd check the tractor and hoe relief settings (there are individual relief valves on my hoe for separate circuits - not just one) and then chock it up to the capability/limitations of your hoe.