Being able to adjust the "chain gap", the distance from the upper (guide) pulley and the freewheel teeth is re4ally important when the freewheel isn't almost too big for the particular derailer.
The idea here is that you want the smallest gap possible without the pulley and cog teeth ever touching, so that the cage movement isn't so much used up by the chain simply angling over. Hence, modern (i.e. relatively super-flexible) chain can be very problematic with certain older derailers that don't closely follow the freewheel's outer profile.
The old Shimano rear derailers, as well as Simplex and some Huret derailers had springs at both the cage pivot and at the mounting bolt pivot, so the derailer body could swing forward and back to better track the outer profile of the freewheel.
Suntour rear derailers on the other hand often had a "B-tension screw" at the mounting bolt pivot which allowed manual adjustment of the derailer body angle (and of the chain gap), but which had an insufficient range of adjustment to closely follow the outer profile of smaller freewheels. I've often removed the B-tension screw entirely and even filed some metal from the "B"-screw's threaded lug in order to allow the derailer to swing forward further (and which swung the upper pulley closer to the cogs.

Older "bushed" chains were quite stiff laterally and didn't require the top pulley to be very close to the freewheel, but different brands of freewheels performed very differently while shifting due to the shape of their teeth.

So in addition to maxing out Suntour derailer's forward swing by removing the B-tension screw and filing metal off of the screw's lug, Shimano and other "dual sprung" derailers can typically be disassembled and with additional holes drilled for the end of one of the pivot springs in order to effect some adjustment of the derailer body angle.
Note that Simplex derailers often featured a locknut where the cage pivot shaft met the outer cage plate, allowing spring tension adjustment at the cage pivot in order to accommodate a wider range of freewheel sizes (size of the largest cog).
Shown below, this Simplex derailer has had it's cage pivot spring tension increased using said locknut with an Allen key to turn and hold the cage pivot shaft during adjustment while the locknut is slackened slightly and then re-secured. This allowed me to retain super-crisp shifting using the smaller 13-24T freewheel that I wanted to use.
You can see the super-close proximity of the top pulley to the freewheel teeth, giving super-responsive shifting even using a flexible, modern, 9s chain.




Lastly, clunky or recalcitrant shifting behavior can also be somewhat the result of things like metal-to-metal contact between the cable and any guide features or cable housings, and even can be due to a poorly- or non-lubricated shift lever pivot (I always disassemble and oil up friction lever's pivoting internals with plain motor oil, which lasts for quite a while as in years). I also affix plastic "spaghetti" tubing/liner material in any metal cable guide groove or tube, securing the liner using compression-fit or with a spot of adhesive (depending on the configuration of the cable guide and also depending on the diameter of plastic tubing I'm using). A fully plastic-lined cable path hugely improves shifting even on friction-shifted bikes!