Do modern guitar amp PCBs still look like they were designed in the 1980's?

[Cerebus]

Using tape it was commong practice to saturate the tape a bit.

Until the mid 70s the standard method of aligning a tape machine was to set the gain for a +4dBm input signal to the point that caused 3% distortion on tape. Input levels during actual recording would be at around -10VU leaving only occasional peaks to experience that 3% distortion. The soft limiting caused by tape wasn't particularly objectionable, you needed good ears to detect it was happening. Some people did indeed deliberately use tape as level compression - if you want to know what that sounded like, listen to any Phil Spector 'wall of sound' recording.

The line-up by distortion level was superseded by an absolute magnetization standard where +4dBm produced 200 nWb/m or 320 nWb/m depending on which standard (NAB or IEC) you were working to. The price of a 2" calibration tape was quite something to behold, as was the weeping of studio managers when they discovered how often those tapes needed replacing.

[mfratus2001]

Well, I repair guitar and audiophile amps nearly every day.
I've worked on literally thousands of amps of all sorts... here is my take.

People like old tube amps because they sound good, and are very reliable. I routinely see 50 year old amps that just need a little TLC, like cleaning the controls and jacks. Even the original tubes are often still working fine.
Tube amps have gone through the same development process as everything else. Point-to-point at first, then eyelet boards, then turret boards, then PCBs. Most companies that care about reliability don't mount their tube sockets on their PCBs. That would be dumb. Most often they are chassis-mounted with the circuit board close by.

There is a mix of products today. "Hand-wired" is a good marketing buzzword, but it really does not mean anything. Everything is wired by hand. We don't have robots agile enough to do it.
Some users are anti-PCB, and that is most often because the boards are laid out by people who have no idea how to properly isolate signals and avoid interaction. Often, it is the ground circuit that is the culprit. I have had to cut PCB traces and re-route grounds on production units just to cure noise and hum.
Most of that is probably from the circuit design person being remote from the actual builder. Probably also the PCB layout person is also remote from both of those. You have to work as a team, and there has to be a closed-loop for performance and quality. The prototypes may sound fine, but production units are often troublesome.

It is hard to integrate digital systems with audio systems. It is hard to integrate solid-state and vacuum tube electronics. But neither of these is impossible.

You can replace tubes, but it is hard to replace transformers and the interactions between the tube or tubes, and the transformer. There are things going on like magnetic saturation and hysteresis that are just really hard to model.
Some modeling amps sound pretty good, some pretty bad. The biggest problem is that they only capture performance at a certain setting of controls. They don't fully simulate the whole amp experience through all variables of input and control settings.

So, PCBs are not the problem. Lack of proper engineering is a problem. Lack of attention in construction practices is a problem. Choices in these that are made just to have good marketing buzz-words is a problem.

Early tube amps were relatively simple. Maybe it is that circuit simplicity that makes them sound so good.