Dumb question: if something is being manufactured on 60nm today, can you not just take the same design and start manufacturing it on 28nm? Or do you need to literally redesign the entire circuit?
An oversimplified ELI5 version is that simply shrinking the size changes the relative electrical characteristics of the pieces of the circuits which may cause the chip to no longer function correctly. This is partly because of physics, since making components of the circuit smaller and smaller affects its electrical properties and increases unwanted electrical effects, and partly because smaller processes require changes in how the chip is made which, in turn, changes the electrical properties of circuit components even if they are the same shape and size as the original.
In almost all cases, switching processes means a complete redesign. 28nm vs 60nm isn't just "we can draw smaller parts now". Lots of other things (silicon doping levels, choice of metal for the routing layers, operating voltage levels, thickness of the insulating layers, ...) change too, requiring design changes to keep the old design working the same way it used to.
A very small set of processes allow one way reuse e.g. you can build a tsmc28hpm design directly in the tsmc28hpc process (but you can't build a 28hpc design in the 28hpm process) - but, for instance, neither of those is directly compatible with the tsmc28hpc+ (note the 'plus' in the name) process. And all 3 of those have the same feature size and are made by the same foundry.
Also, 28nm pays a huge price in mask complexity etc over 40/65nm. So its cost per area is much higher. This works out to a win if your area gets smaller... or a massive loss if it doesn't. And if you just draw the same features with a different process, guess what, your chip cost just doubled (or whatever it is, depending on the particular processes) on the "more cost effective" process.
Chip designs have multiple layers of abstraction to represent a "circuit". Moving from 60nm to 28nm, your RTL is probably fine, but the physical layout will need some reworking as the transitors have different characteristics, SRAM different latencies, etc. It could be more cost effective to also rework some of your RTL, depending on your volume.
IBM introduced copper interconnects in 1997; the designs before that date were aluminum. IBM is now doing the same thing with "gate-all-around" that will replace FinFET, which itself replaced planar.
You can't take a tube radio and manufacture it with opamps without substantial design changes.
Samsung is starting to use GAA right now, and TSMC will use it for the next process node.
No, you'd need to invest a lot of labor to port the design over. Factors like area, power, gate voltages can be completely different even between technologies on the same node (for example Global Foundaries 28nm is likely completely different than TSMC 28nm, aside from the feature size).
You need to redesign the entire circuit. If it is completely standard digital (e.g. no RAM, no Flash, no 3V IO, no ESD structure), then you can likely port it without too much pain. However, you still have to change the entire package/bond pattern, and completely requalify the part with a customer who sees no advantage. Minimum port/design cost $1M and expect mask fees of at least $2M.
So at 30% margins on a $0.33 part, you can expect to break even 30M sales later!
Neat trivia: Intel recently backported a microarchitecture to a bigger node to cope with fab issues at the time. The 11th gen "Rocket Lake" parts are a 14nm backport of the 10nm Ice Lake processors.
From what I understand, doing so was no small effort and is considered a strong triumph for the team that accomplished it.