The commercial modular amps are interesting. I've never had a chance to try one. They seem pretty rare.
I'm thinking that a modular approach would be useful to use in a studio where chasing tone and options are is so important. Being able to plug in different tone stages is useful. Same for different pre-amp stages. It can help keep the signal path uncluttered. Modular design is common in recording consoles because so much is repeated and it helps with service turnaround. Downtime can be expensive.
There are some interesting images of a channel strip designed by EMI like the ones used at Abbey Road:
http://vintageking.com/blog/2015/11/emi-strip. They used a combination of printed circuit boards with small turrets. The TG12345 is a transistor based design. You can see the bus lines running perpendicular to the boards. They sure knew how to build a good sounding desk.
A modular approach is helpful in designing amps. Switching in and out modules helps quickly A/B different approaches. It's also nice to have a sub-assembly handy in case you want to try it. Circuit boards are nice but a fast turnaround and multiple revisions gets costly fast. Circuit boards are done closer towards the end. Turrets are attractive because they are fast and dirty.
I know what you mean about those older consumer products that used wire wrap pins on the circuit boards for external connections. Some of them were fairly low end. Using wire wrap certainly cut down on manufacturing time and cost. Today we have a lot of good quality connectors that can serve that purpose.
I have a Mesa Boogie amp that has all kinds options. I tend to dial in a good tone and leave it. The amp is complicated and it takes time to muck around with it. Overly complex can be a negative.