Why were hobbyists advised to socket ICs before, but not now?
Paul I'm going to go out on a limb here and try to answer this.

In my experience, the 80's era and prior did use sockets quite often for everything from IC's to transistors. There may have been several good reasons for this:


If the part failed, a socket simplified repair.
Most IC's were DIP package (relatively low pin-count) so could be socketed easily.
Older designs were engineered for serviceability, not lowest cost.
If you botched one pin, replacing a socket was inexpensive compared to the IC.
Newer versions of the IC could easily be "upgraded."
Early-production parts may have been slightly less reliable (opinion.)
Yes, soldering the socket prevents thermal damage to the component.
Soldering irons of that era were larger - 35W or more - hence a socket.
The IC could be removed and swapped out to test (or put in your other gadget.)
Full-fledged circuit simulators of the time were not very robust, if available at all. If any design calculation error crept into the PCB, it meant troubleshooting hardware.


At the onset of the electronic revolution the costs were high so focus was more on quality workmanship and serviceability. Nobody really knew how long a fancy new transistor would work in service - so they often built them way over-spec. Transistors rated for 10A could routinely tolerate 15A and survive. 

Today the situation is exactly the opposite - costs are low, production is lean, and all the corners that can be cut, are. We have great data now on exactly how well devices work in the field, and have trimmed much of the "headroom" off component specification, both figuratively and literally. If you try to pass 15A through a 10A device today, it'll surely be damaged. Not only that, but we have a good idea where the technology is going today, and can make good predictions on how long a device will remain in service. For those components which might be prone to failure, many DIP and other larger packages are still available, should the engineer choose to use them.

Today we'd use no socket/SMT for the following reasons:


No need to drill the PCB.
No need to plate any through-hole connection (optional at home.)
"Jellybean" parts are incredibly inexpensive today - if you damage one, scrap it.
Modern IC's can have hundreds of pins and dozens of form factors - making DIP obsolete and impractical for them all. (Let alone the increased speeds and all that entails.)
Modern IC's are much smaller. This may be perceived as a hinderance to the hobbyist, but is the whole reason our cellphones are even possible. Luckily, many devices still exist in DIP packages. For those that do not, expander boards are often available.
New designs are less-engineered for serviceability, and more as "throw-away" devices. (Good point @dim, added.)
Modern simulators can offload much of the "did I get all my maths right?" into the click of a button - oops that resistor needs to be 10x larger, oops that op-amp exhibits saturation on it's negative rail - before even building a PCB. (Thanks @Ali Chen.)
Instead of 35W irons which can easily lift traces, temperature-controlled irons and/or hot-air is used, which makes soldering safer, faster, and easier.
SMT lends itself better to mass-production. A socket is just another step someone has to take in handling, which costs money.


Less work, faster results - the mantra of the new millennium. I believe that's why we've moved away from most through-hole and socketed designs today. 

I used to make my own PCB's; it was fun for small projects. Perchlorate, ferric chloride, developer, toner, even cupric chloride - tried them all. Satisfying? I guess so, but today I'd much rather send my design files along with less money than I would have spent to do it myself, and still end up with a better product. Efficiency has become paramount.

While components are getting smaller and smaller, the PCB details must match. Sure, one could get pretty good results with the laser-toner transfer method at home, but it would be risky for something with a very fine pitch such as a VQFN. (Yes, even those can be soldered by a hobbyist - only need a hot-air gun, solder paste and some flux. (And likely some kind of magnifying lens.) There are many videos out there on the subject, some even using traditional irons. (Try a hot-air station; you'll love it.)

Edited to reflect changes to question.