One factor is that the other SMG issued to British forces, the 'Lanchester', was chambered for 9x19mm ("9mm parabellum/Luger"). The then-new Browning Hi-Power pistols were chambered for 9x19 also. Ammo commonality is one factor behind the STEN being chambered for this cartridge.

Another is that the STEN was a lightweight design, intended to require few materials in order to make it viable for Britain's war economy (and viable as a guerilla weapon). Having a less powerful cartridge than .45 ACP makes this easier, as the firearm requires less raw materials to retain its structural integrity ('falling apart'). Most configurations of the STEN were about half a kg lighter than the M3, and almost 2 kgs lighter than the Thompson series.

It is interesting that you ask about 'enemy ammo', since this contemporary article from 'Collier's Magazine' (September 1943) claims that

"The same [9-mm cartridge] is used by the Nazi, Italian and Japanese armies. This meant that captured Axis bullets could be used, tremendously reducing the problem of a supply. At the same time they put a nick into the rim of their 9-mm cartridges, which makes it impossible for the Axis to use their ammunition without replacing all the ejectors in their guns. Now that the defence of Britain is no longer a problem and the Allies are about to invade Europe, this feature makes the Sten doubly valuable, for the underground armies can supply themselves with captured ammunition...."

I can't find anything to support this claim, and I suspect it is nonsense, but it's interesting anyway.

Source and further reading; Leroy Thompson (2012), 'The Sten Gun'. Osprey.

It was meant to be cheap and easy to build or repair in the field from expedient materials. Ammo is not really something that can be made in the field, but you can certainly take ammo off of dead Germans.

The thinking is the same as the .45 liberator that the US dropped behind enemy lines: you use it to kill a German and then capture his weapons and ammo.

So if you kill a guy that has say four mags, rather than have one gun with four mags, you make a sten or two and have two guns with two mags each, or four guns with one mag each and so on.

Also, the sten is an insurgent's weapon. These guys weren't going out, killing a patrol, and then going back for resupply. They were in the field for weeks at a time and if you run out of ammo, you're boned. The Germans were relatively well supplied with bases all over the place.

From "The Guns of Dagenham" about The Sterling Engineering Co of Dagenham, who made Lanchesters, Patchets and De Lisle carbines during WW2 and later Sterling SMGs and Armalite AR-18s.

In 1940 the Chief Inspector of Small Arms was given 2 commercially bought German-made MP28s to evaluate, with the intention of manufacturing a British SMG. It had been suggested that .38" ammunition should be used. The .38" was current standard issue ammunition for the Enfield No.2 revolver; it was a rimmed cartridge and unsuitable for an SMG. An officer of the Ordnance Board advised that a 9mm round would penetrate seven 1" deal planks at 100 yards and five 1" planks at 200 yards. A .38" round would only penetrate two 1" deal planks at 50 yards. The decision was made to use the 9mm cartridge for the new SMG, the Lanchester, which virtually a direct copy of the MP28.

With the Sten, a decision was made make the weapon capable of using MP40 magazines and the same 9mm ammunition. The MP40 and Sten mags were double-row, single-feed and this introduced the main weakness of the Sten. The magazine lips had to centre the top round in the mag and they were easily bent.

The Sten was supplied in huge numbers to partisans later in the war but, at the time of its design in 1940, the intention was to provide a cheap, plentiful weapon for British and Commonwealth forces in the context of the threat of imminent invasion by the Germans and after the retreat from Dunkirk (and the loss of much equipment.