During WWI the central powers turned pistols/handguns into semi and fully automatic weapons. Germany turned the Luger PO8 into a carbine/short rifle type thing. Austria-Hungary turned the Steyr M1912 into two different fully automatics, the Dopperpistole and the Repetierpistole. They also turned the frommerstop into a fully automatic gun. Why didn’t the allies turn any handguns into automatic rifles and SMGs?
Because of two factors.
The fully automatic handguns are utterly useless in 99.9% of cases. They are impossible to control and aim, due to the high rate of fire coupled with the handgun being too small to provide the extra mass to dampen the recoil. Once you press that trigger, the bullets start spraying everywhere and you run out very fast. They may be OK for a very close quarters situation, but even there you'd be better off with a shotgun (which the Allies did use to clear trenches). There's very few fully automatic handguns today (G-18 is a prime example), and for a good reason.
Nobody expected the warfare to be done the way it turned. Trench warfare, close quarter combat (which wasn't all that common anyway). The development of fully automatic pistols was just a fad largely limited to two countries which were very close culturally and shared the same language and the same border and often the same fads (Frommer is a Hungarian pistol and Hungary was part of Austria-Hungary back then).
Now, SMG is a different thing. MP18 was a truly revolutionary weapon perfected for trench warfare. But even though SMGs use pistol ammo, they are not pistols.
I can't really speak for handgun development, but the machine-pistols you mentioned were very limited production at best and never really saw any significant service. The stocked pistols like the Luger you mentioned, or, perhaps more famously, the Mauser C96, were a more common concept that predated the war and wasn't exclusive to Central Powers manufacturers. FN in particular was producing the Model 1903 complete with shoulder stocks prior to WW1, and about 11,000 of these had been ordered by the Russian Empire prior to the outbreak of war, complete with shoulder stock.
As far as production of automatic weapons goes, the focus of the Entente appears to have been on automatic rifles rather than machinepistols. The British Lewis and French Chauchat automatic rifles were guns for which the Central Powers really had no answer or analog. Perhaps most unique was the Italian Villar Perosa, which was originally designed for aircraft use but was quickly co-opted for infantry. All of these weapons began to appear on the battlefield in 1915. The Villar Perosa in particular stood out because its use of pistol ammunition arguably makes it one of the first submachineguns, although its role on the battlefield generally wasn't one traditionally associated with submachineguns. Developments across the Atlantic in the form of the Browning Model 1918 and Pedersen Device further point to a focus on automatic rifles rather than pistol carbines and automatic pistols among the Entente powers.