What PC has a +4? That's a 1st level trained PC with a +2 stat bonus. That's probably the lowest difference you will find.
There are 18 skills, most classes are trained in 2 your background affords another 2. That leaves the vast majority, 14 of the 18 skills (78%), untrained for most PCs.
The lowest difference you will find is negative, +4 or greater difference is going to be uncommon. If the PC is playing a Rogue there can will be a maximum of 6 skills with greater a +5 or greater difference with a 16 ability score in tier 1 and then in the other 12 skills there will be less than a +5 difference, to a minimum difference of -1.
Also let's remember a 1st level Fighter is also proficient in 4 skills and only one of those 4 can be based on Strength.
A +5 at 1st level isn't that difficult to get after all, and add on something like Guidance and now I'm +7 to +10 compared to +2-+5.
It is difficult to get in more than a few skills in tier 1 and that +5 only applies to those small number of skills.
Guidance stacks with Tactical Mind so it is irrelevant and that would make it +6 to +9, that is not a difference unless you are talking about a PC class that can cast Guidance on themselves, and that would only apply to a Cleric which has generally poor skill options for either the exploration or social pillars.
So, yes, in your theorycrafted white room where the incompetent character (+0) is competing with a 1st level barely competent character, Tactical Mind is great.
This is rich. You are the one theory crafting in the white room, not me!
You are on here saying an ability you did not know even existed and have never seen in play is not powerful and you are not using any statistics, examples or mathematics to even back it up that claim, just attacking other people's assertions when they explain how they have seen it used in play and how it is mathematically powerful.
I am using statistics and examples from play. Neither of these is whiteroom theory crafting.
And I'm sorry, but a single 2nd level spell which is pretty common, which will almost never be cast in combat when the casting time will matter is not a "lot more costly".
I don't think you really are sorry.
Stealth (and other skill checks) will be used in combat and when they are used there is no action economy involved in applying the bonus from Tactical Mind. That is the point!
The reason Pass Without Trace won't be used in combat is because it takes an action to cast. If my PC is trying to hide this turn, in combat, casting Pass Without Trace does not help due to the action cost, neither does Guidance. Other abilities, like Tactical Mind, Favored by the Gods, Lucky, Inspired Eclipse, Skulker etc are all much less powerful than PWT for making stealth checks but they do help that PC hide in combat better due to their lower action cost. That is why the difference in action cost matters.