I'm not the "go to" guy on these but I will offer an opinion anyway. Can't resist:>)
As far as diaphragms (or any other mechanical device) going bad, yes, it can. The diaphragm can rupture or the actuator rod can stick.
However, in this case, the diaphragm is known as a "dashpot" by many of us mechanics and typically has nothing to do with starting or fuel enrichment. The PRI designation does not stand for "prime". If you look further down the parts list you will see another PRI designation associated with a throttle cable "stay"
(bracket) and THAT item is completely removed from any fuel flow reference.
Dashpots are employed as anti-stall devices and used to briefly hold the carburetor throttle plates open when the throttle control is rapidly pulled back from high speed settings to keep the engine running.
As to your complaint, I would more likely suspect that some other component or engine wear is probably causing this. A couple of suggestions would be:
Spark plugs....when were they last replaced?
Valve lash.....when were the valves last adjusted?
Those are two items I would check first for this. Plugs do wear and the spark gap widens over time.
Valve faces slowly sink into their seats and can change (close) the rocker to stem gap.
Both can and will alter the way the engine starts and idles.
And, of course, carburetors do get deposits built up internally over time and cause similar issues.
But my first two suspects are plugs and valve adjustment.
Good luck.
