Yes, once microcomputers started to be become popular that was the way most programmers went. And having the high-level control-software / user interface on a computer, generally allows much-easier upgrading for newer programmable IC's.
Some of these particular non stand-alone but computer-controlled programmer models originally had proprietary interfaces for specific computers, that required a special interface ISA etc. card in PC's or were designed specifically for various home computers like Acorn, Sinclair etc. - Although those directly on a fairly high-speed bus, could allow direct-control of the programmer's timing, so they didn't always need their own internal microcontroller.
However the more professional / industrial end ones like Stag, Elan, Data I/O (and GP Electronics ones that it seems was the original company that was manufacturing the Softy-1 before Dataman produced the S2 etc.) were usually fully stand-alone, with their own Keypad & display for editing its own RAM Buffer - Although usually with a serial interface for transferring data in & out (Data I/O, formed in 1969, even had paper-tape storage integrated into an early one:
https://en.wikipedia.org/wiki/Data_I/O), as these were developed before microcomputers so only had very-expensive mainframes & mini-computers. A lot of these can be found on this resources page:
http://matthieu.benoit.free.fr/
But upgrading these stand-alone ones would usually involve swapping EPROM's (although sometimes in a plug-in cartridge).
Most Parallel-port and all serial-port & USB controlled Programmers did need their own internal micro-controller. But this was basically doing all the timing-critical pin-driving and they were designed to be used in conjunction with a computer running control-software with all the required prog. IC support.
Stand-alone units did still have their uses many years later (and I had originally intended to control my BBC Computer controlled design with a Z80 and Keypad + LCD Display so you didn't need an expensive at the time BBC), particular where a computer wasn't available.
The 'Softy' S3 and then S4 were quite popular, as these were now battery-powered hand-held units that you could load a device library EPROM into RAM to upgrade device support. Plus they now had an RS-232 serial-interface added, for file transferring and still had the ability to emulate and EPROM - Now on a separate connector. So they could be ideal for field-use developmemt / upgrades.
But Dataman 'replaced' the S4 with the 'S6' which was just a small USB-Controlled programmer with no EPROM-Emulation and needed a Laptop etc to use it. So used S4's are still quite sought-after, as it seems no-one else has made anything similar. And Dataman still sell some spares / provide the software online for the S3 & S4.
EPROM's and One-Time Programmable IC's are now generally all obsolete, having been replaced by FLASH. And most of these (Inc. FLASH built into microcontrollers) are now In-Circuit/System programmed with a Standard JTAG or SPI / I2C style serial interface for all devices.
So ultimately it could be the end of the line for programmers that directly program the IC by itself, with many required adaptors. With maybe only mass-production wanting the IC's pre-programmed to save time / needing to attach ISP programmers to the board.