The engine compartments are smaller, and the engines have more parts which means it takes longer. However if you can hook up and read the OBD2 system codes you get a lot of diagnostic info that was never previously available. This can mean you send a lot less time redoing work. The real limiting factor is space. If you're not averse to Quora, there's a nice discussion here https://www.quora.com/Why-are-modern-vehicles-so-difficult-t....
By the mid 90s things settled down and were much simplified, thanks to the computers and electrification of most actuators. You just treat the engine control module as a black box, with a small handful of easily tested sensors.
I'd take any 90s car over most post-smog ~pre-obd era vehicles, your father's complaint strikes me as more an irrational fear of computers. There's a definite sweet spot in the 90s where computerized cars still have throttle cables but extremely simple and minimalist computerized engine control systems vs. years prior.
Yes, cars got a lot more complicated. Yes, there are a few parts on them that the shadetree mechanic has no chance of fixing on their own, such as an automatic transmission or the car's security system. (Those parts, you either replace the whole modular unit, or pay a specialist/dealership to repair.)
But for the most part, they are still _systems_ and they are still _understandable_ and repairable. The key is that you have to have the willingness to learn how these newfangled systems work. To make it a computer analogy, it's like an old COBOL programmer complaining that you can't fix modern computer programmers because everything is Javascript now.
It's my observation that over the decades, the mechanical components of cars (the engine and transmission) have gotten extremely reliable while the electrical and computer systems are where most problems occur. That means you have to understand the basics of electronics and electricity in order to troubleshoot these kinds of issues. I know a few motorcycle guys who can rebuild a whole engine for fun on a lazy Sunday afternoon, but the moment there's a slight electrical problem with the bike, they throw their hands up and trailer it into a shop.
On the diagnostic front, the good news is that auto makers have standardized on a lot of things that actually make it _easier_ for independent shops and home-gamers to work on modern cars. For instance, all cars have an ODBII port and CAN bus through which you can (at a minimum) read diagnostic codes and read live data through with a dirt-cheap reader. More advanced scan tools can graph live data from every sensor on the car, communicate with the car's various modules, perform diagnostics, and other fun things. These cost more of course (hundreds of dollars) but can still cost under one trip to the repair shop depending on the issue if you're willing to put in the effort and time.