They are very robust small lathes that had high precision when built. They are small form factor and many operate on single phase power, both attributes that many small/home shops prefer. They are powerful for their size in spindle HP and have a really large saddle, The base and bed foundation are designed to preserve integrity with three simple points of contact. The belt driven variable speed spindle is smooth at any speed from dead slow to max RPM 2500~4000 nominally. These lathes have a huge number of pluses, the one weak spot is the tailstock. It can be argued that they are a small toolroom lathe and the tailstock is adequate but, a bit more beef here would go far.
The 10EE is not the most ergonomic lathe but the controls are well placed. The level of engineering, fit and finish are top notch. There are other small lathes with similar features, most were produced in small numbers many in Europe. There were but a handful of domestic competitors for the 10EE. The success of the line and total numbers produced make the 10EE more accessible than its imitators and rivals. The 10EE was originally developed long before many of the other lathes in this class, some have been doing good work for over 80 years. That alone is quite a legacy but, you can still buy a 10EE new or at least newish right from the source. The 10EE was never a price point machine, it was very expensive from the start. Companies and government agencies that bought these valued the performance of these in spite of the cost. My 10EE in 1976 cost more than a nice home in a good neighborhood of Los Angeles at the time.
Then there is the "look" that art-deco stylized form is just industrial design at its acme. Machine tool builders were aware of aesthetics in the lathe 19th century into the early 20th century. Somewhere along the line it became less relevant, WWII may have been a contributor. Pre war many machines had graceful flowing lines. The 10EE as a legacy of a former era kept its curves as it matured post war. There were other machines that were styled after the war but the 10EE has a classic profile that was instantly recognizable. Monarch modified and updated the 10EE with tasteful amendments that preserved the original design elements. The combination of capabilities and design are perhaps why these little lathes are so sought after. That they built tens of thousands didn't hurt.
Steve