Circa '63, IBM systems were generally considered the natural choice for timesharing at Project MAC. After all, CTSS had been implemented on the IBM 7094 and IBM had a close relationship with MIT.
But despite MAC's lobbying, System/360 left out virtual memory, signalling that IBM was focussed more on their commercial batch systems than on the smaller university/scientific market.
GE's 635, on the other hand, had privilege rings and virtual memory built-in. So did the DEC PDP-6 (in a primitive form). So those are the machines Project MAC purchased.
Now MIT might not have been a big source of revenue for IBM but it was still a star customer from an image perspective. And IBM realized the error of their ways pretty quickly, and got a crash program going to modify the Model 65 with paging, which was out by 1966. But they were too late, really. GE, DEC and a bunch of other companies were already eating into the timeshare market aggressively.
If the original higher-end IBM System/360 machines had included paging hardware from the start, the history of computing could have indeed gone very differently.
Actually the 635 had no virtual memory or I think even memory protection (no more than the IBM 7090 it was closely modeled after). The difference was that GE promised to add the all-singing, all-dancing MMU (paging, segmentation, rings) of MIT's dreams so they won the contract, resulting in the Multics 645.
The problem long term was that while every MMU option was available, the Multics base platform remained an extended, async 7090 (itself an extended (circa 1952) 704), rapidly falling behind in performance (and ability to be re-implemented quickly/well in rapidly advancing technology). Look at the trajectory from 645 to 6080 to DPS8 and shudder. Compare with the 360 as a modern ISA re/implemented at close to the state of the art.
Multics proper became excellent, highly capable software but to use the term the Germans used about Austria-Hungary in WW1, it was "shackled to a corpse".
1966? Good. There was, in about 1967, the IBM 360/67 with 31 (up from the usual 24) bit addressing, virtual memory, and virtual machine software CP67 (Control Program 67) and interactive shell CMS (Conversational Monitor System).
Later of course, CP67/CMS became VM/CMS (Virtual Machine CMS) which was actually a big deal for IBM for decades if not to the present.
IIRC CP67/CMS was written at IBM's Cambridge Scientific Center, supposedly as a tool for operating system development. But by 1973, a company in Stamford, CT, NCSS (National CSS), was selling general purpose time-sharing service on 360/67 with CP67/CMS via just dial-up communications.
So, could log on and get ones own virtual machine, complete with a software command IPO (initial program load), the button on the front of the 360 machines. Then logged on could write and run assembler (made writing assembler surprisingly easy), PL/I, etc. If the software hit a bug with, say, an infinite loop, then could use IPO to start over!
NCSS service was popular around DC, and NCSS had an office in VA just over Key Bridge from DC with a leased phone line connection back to CT for a line printer. So, if wanted to print out a stack of paper 1" thick, could do that!
NCSS service was not cheap, but due to the Cold War and the Space Race there was plenty of money sloshing around DC for paying the NCSS bills.
IIRC in 1973 it was 6000 lines of typing in PL/I at NCSS that scheduled the fleet at FedEx, alleviated some concerns of the BoD, enabled some crucial funding, "Solved the most important problem facing the start of Federal Express" (COB F. Smith), and essentially saved the company (once of at least two times the company got saved).
By 1974, Brown University, especially its Division of Applied Mathematics, had a CP67/CMS system essentially donated by Tom Watson, Jr., who had gone to Brown. Brown instrumented the system to collect data on its operations. Statistician U. Grenander did a lot of statistical work with that data. He remarked, IRCC, that the data from the computer operations "looked nothing like biomedical data" he and statistics had long been used to.
And IBM's System/370 upgrade from System/360 had essentially all the 370/67 hardware features together with virtual machine assist that made some of the virtual machine faking faster.
Prime had an hierarchical file system in the 1970s, but as late as 1994 at IBM's Watson lab VM/CMS still didn't have hierarchies in the file system. As a partial alleviation, could have virtual disks, each with a drive letter.
Of course eventually the Multics ideas of authentication, capabilities, and access control lists made their way into IBM's RACF (Resource Access Control Facility) and much more generally in computing, e.g., with authentication via MIT's Kerberos with RSA (Rivest, Shamir, Adelman) public key encryption.
To me what is amazing are (i) a lot of concepts from those days are still with us, (ii) can buy, on-line, quantity 1, e.g., for about $100 an AMD FX-8350 processor with 8 cores, 64 bit addressing, and a standard clock speed of 4.0 GHz, (iii) can get at a small home office up/download Internet data rates of 1 Gbps for some reasonable price, say, $100 a month, and (iv) the early players IBM, GE, Honeywell, Prime, DEC, Data General, and more are no longer involved or are taking a back seat against QUALCOMM, Intel, AMD, Applied Materials, TSMC, Cisco, Microsoft, Apple, etc.
That strikes me as being one of those pivotal moments in computing history.