There were many different types of mortar - America used 2 different types of 60mm - the Mortar M2 on Mount M2 was the "standard" bipod fired version based on a design from Brandt (as were most mortars in the world at the time). There was also the mortar M19 on Mount M1 which was much like the Japanese "Knee" mortar - ie only a barrel mounted to a small curved baseplate.
The Bipod mounted version had no means of holding the mortar on target appart from the bipod - it just had the ball mount on the base plate, so any "free tubing" as discussed would probably have been horribly inaccurate.
The notes I have for the M19 mortar say it wasn't bery accurate and had limited range, and was limited to small numbers issed to airborne and special purposes units.
The Russians had 4 versions of 50mm mortars - 3 of them had "standard" bipods but were much lighter than the US 60mm (19kg vs 9-16kg). Their final one did away with hte bipod for an all-in-one baseplate/traverse mechanism. There were only 2 elevations - 45 or 75 deg, range being varied by venting exhaust gasses forwards from a tube under the barrel.
The Brit 2" was mostly used for smoke than HE support (BTS note!! ), was triger fired and indeed could be fired horizontally - but not loaded that way!!
Perhaps the most bizarre light mortar was the Italian 45mm which was breach loaded and the propelling charges came in magazines of 10. A lever opened the breach for the bomb, and closing hte breach automatically loaded a charge. Apparently hte rate of fire was very high, and accuracy excellent, but the bomb only weighed 1 lb, which was only 1/2 to 2/3 the weight of other light moratrs - the Polish 46mm for example weighed 1.5 lb, the British 2" 2.2 lb, the Jap 50mm grenades 1.17 and 1.75 lb. The French 60mm had a havy bomb weighing 4.5 lbs.
Almost forgot the Russian 37mm spade moratr - imagine a simple spade with a square blade and a simple straight handle - well the blade was the baseplate, the handle hte barrel. A monopod was formed by the plug that closed the barrel when configred as a spade!!
Hope this has all amused and informed.
Mike