

There is an aftermarket for F-16 planes and their spare parts.
Also, I should note that Iran (of all countries) is still flying its F-14 Tomcats, unless I’m mistaken.
The most immediate effect is ceasing updates for then AN/ALQ-131 countermeasures pod. If Russians come with a new radar or make their existing weapons behave differently, this could have considerable effect on the survivability of an F-16 in a hot situation.
Note: Iran still uses F-14 Tomcats.
Possibilities for implanting a logic bomb are endless, but there are still no case reports about an US-originating plane becoming remotely disabled.
(Russians would absolutely like to listen to a message which accomplishes that, meanwhile allies would definitely want ot change encryption keys on any plane which is supposed to receive that. I also don’t think that military planes will accept unencrypted messages. And their communications subsystems are separate subsystems, which can be disabled or replaced.)
Meanwhile, in a hypothetical doomsday scenario, Danish F-35s would land (or be unloaded from a container) in China, and be greeted with cheers, red banners and golden confetti. Damage to the US would far exceed anything that Denmark could do by firing something.
Note: these are scenarios which are not supposed to happen, but dramatic loss of trust among allies can actually result in that - if country A backstabs country D, there is nothing that really prevents D from betraying A to C.