Apparently NOT in the minds of the EAxians! But fortunately, AncientHighway came up with the solution: he wrote a mod - ah-tinkeringskillsmechanical - which added just that! However, when I put that mod in my game, any sim who had at least one point of Tinkering enthusiasm, would not be able to Tinker at all anymore: anytime when I ordered them to Tinker, they would just jump, and be reset!
So I opened up AH's mod, and investigated the issue. The search required me to investigate Skill- and Enthusiasm-gain in general as well, so I dove into the objects.package too. My search was successful: sims can now Tinker as much as they like, but they will not jump anymore!
Then I noticed something else: while this worked on kitchen appliances, bath tubs, showers, stereos and TVs, it did NOT do any good for sims tinkering with the Exerto 5000 Multipress Excercise Machine, any of the Hot Tubs, or the Modular Synth. They were simply never included in AH's mod. So I went on another mission, and included those into the mod as well.
So now I bring you BO - Skill while Tinkering. With this mod, whenever a sim is Tinkering, they will gain Mechanical skill.
NOTE: If you do NOT have FreeTime installed, there's no need for you to install this mod, because your sims won't be able to tinker anyway!