Growing up in Germany it was weird to think if these weapons or similar ones were ever used it would probably mean that Germany and probably parts of Europe would be destroyed. Pretty scary.
One problem with nuclear mines is that they're unattended. If some crazy circumstance happens where the US loses control over the area, but it's not war, then you suddenly have a bunch of hidden nukes lying around that could detonate.
Another problem is that if the Soviets ever found them then they could use them as effective propaganda. If even one of those mines goes off, then they could say that they're liberating the Germans from their American oppressors. After all, you don't nuke your own ally and a nuclear detonation is hard to hide.
That was really the defining philosophy of the Cold War nuclear threat escalation; total extermination of millions of civilians in as short a time as possible.
The "strategic nukes" on the other hand, are city-destroyers. 10Megatons or bigger, 100x or 10,000x larger than tactical nukes.
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In effect: a tactical nuclear weapon is fired even if there are friendly forces nearby. In contrast, strategic nukes are fired when you want to kill everybody in an area.
Even if a serious war started, no sane person would ever dare to touch strategic nukes. Once strategic nukes start flying, its pretty much the end of the world as we know it. The only response to a strategic nuke is to follow through with MAD.
Tactical nukes are small enough that MAD may not be triggered. It would be an unprecedented escalation, but military generals around the world would quickly try to draw the line at "tactical nukes only". The problem is that no one has really drawn a hard line at what makes a nuke "strategic" or "tactical"... there's a smooth curve from 10 Tons (Davy Crockett) all the way up to Tsar Bomba (50,000,000 Tons). So there's a big fear that starting even with small tactical weapons would lead to a path of escalation towards the biggest nukes.
You're a commander of a small airfield in the Pacific and the last you heard from the US was that tactical nukes had been used in Europe. Now, communications are down. You have a bunch of planes ready to go, and if there's missiles or planes headed your way, you'll die pointlessly if you don't put them in the air. You have a letter from the President authorizing you to launch in this situation.
Now what?
If you hear the boom and you're not dead... then it was probably tactical.
Strategic nukes aren't launched one-at-a-time. They'll be launched thousands-at-a-time. You're simply dead, you'll be pulvarized by multiple ICBMs before you even know what hit you.
The plan is to launch your strategic nukes in retaliation BEFORE they hit their targets. Alternatively, you have enough secret nuclear submarines to launch your strategic counter-attack after-the-fact (even if the mainland is destroyed).
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The launching of any ICBM would probably trigger the end of the world as we know it. ICBMs fly at such speeds that they cannot be reliably stopped: they're basically spacecraft. Once launched, their target is effectively going to be destroyed within 10-minutes or so.
The real risk of strategic weapons is misidentifying a flock of birds as an ICBM (or other such technical glitch).
According to Ellsberg, there was a period where there was no actual plan to defend Europe by other means than massive nuclear retaliation.
https://www.amazon.com/Doomsday-Machine-Confessions-Nuclear-...
You're probably too young to remember, but Germany was a very hot frontier at the time and the most probable point for battles on the ground as opposed to ICBMs or subs.
The answer wasn't as clear as with a ICBM attack, that was a much more irreversible decision.
So US strategy was build around using their nuclear advantage to stop a conventional Soviet invasion of Europe before it could get out of Germany. Hence the development of tactical nuclear weapons like the M65, which seem bizarre to us today, as we're used to thinking about nuclear war in terms of MAD, but made sense (or at least, more sense) at the time.