iMac mid2017 Mojave crashes after clean install

Every time it crashes I have to unplug the power supply to reset the SMC or it will not reboot.

That's an indication of a bad power supply. Had the same problem occur with a 27" iMac. Had to unplug the power cord before it would reboot. It was under warranty but took 3 trips to the Genius Bar and several sessions with Apple engineers via phone before it got fixed.

They wanted to make sure the problem wasn't software related and finally had me erase the drive and reinstall the system without migrating any of my data over from Time Machine. When it kept crashing with a new, pristine system they went ahead and replaced the power supply

If your Mac is in warranty make sure it has a current backup (a clone to an external HD is very good for this type of restore), make an appointment with the nearest Genius Bar and have them test it and, if necessary, erase the HD and install a new, pristine system. Might save you a couple of trips.

If it's not in warranty I'd make an appointment to have the power supply replaced right off the bat. For course have them run their tests but give them authorization to replace the power supply.

Good luck.

Since it's out of warranty you might want to investigate it at little more before going in for service. Make sure all peripherals except your keyboard and mouse are disconnected. Also, I am very concerned about the RAM since obviously you have upgraded that. I would drop down to just 1 or 2 sticks. The fact it crashes so hard you have to do an SMC reset to get it to reboot suggests it could be that added RAM (or the stock RAM) causing the problem.

Does the hardware test give you the option to test the RAM optionally, and did you do that? Even if so and it passed I am still concerned about it.

I would also boot up in Recovery Mode and try the Get Support feature which basically gives you a Safari single-tab browser and try using that for a couple hours to see if Recovery mode itself works ok.

If the safari-in-recovery works OK, but the problem still happens even dropped down to just the stock, or just the upgraded (stock removed) RAM, it may be worth looking at the console logs to see what is going on. It would also be helpful to know that if you just boot up your Mac and don't do anything, if it crashes after a time or is fine until you start doing things. It would also be good to know it only crashes when it's getting pushed and the fan is in high gear that it crashes, or if it crashes even with minimal activity.

You did mention Safe Mode. Specifically have you tried to use Safe Mode for a couple hours and does it crash in there as well, or no? Although RAM is still my number one suspect it could be your SSD (or the power supply, as suggested already).

You could try installing macOS via Recovery Mode onto an external USB and see if that works much better (which would indicate a possible internal SSD/Hard Drive issue) or not.

Personally, I would do all these suggestions before taking it in for out-of-warranty service.

In terms of "crashes" being more frequent, what does it do when it crash? Error screen, Apple logo, black screen, or power off?

If it's a power off crash and there is overheating, that would definitely be bad to keep turning it on. If it takes 5-15 minutes to power-off crash first thing in the morning, but 30 seconds to a minute or 2 if you immediately come back after a previous crash, that's a dangerous sign of the CPU failsafe cutting in and shutting off the power due to overheating/bad fan.