A better way would simply be to suppose that mines are factored into the daily consumption of supplies. Your idea would add some pointless micromanagement that simply has no place in a grand strategy game. I can't think of a single time when the leader of a nation (Stalin, Churchill, Roosevelt, Hitler etc.) had to specifically order a division or brigade to deploy their mines and field fortifications. The decision to create a minefield is, at its' highest, a decision for a divisional commander, but more likely a battalion or company commander will make the decision to deploy mines. Having the player click a button for each time they want a unit dug in with mines would create an insane clickfest for time when you want to fortify your entire front, such as might happen in 41-43 during Winter on the East Front.
At Kursk and El Alamein, anti-vehicle mines were laid in their tens and hundreds of thousands, and had a strategic impact. It didn't happen often, but when it did happen, it happened in ways that impacted materially on battles that are seen as turning points in the war. Landmines were in all likelihood more important than Germany's Tigers at Kursk (and far more important than their Ferdinands, which are both modelled in the game). As for Stalin, Churchill et al ordering the deployment, the vast majority of things the player does in HoI wouldn't have been ordered at that level, so that's neither here nor there.
And in terms of landmines, I'm not arguing for player intervention whenever they're used, but rather whenever extensive concentrations of them are used. Landmines would have been used in most defensive situations, but only in a specific number of situations did the defenders 'go large'. These situations should be relatively rare, and also somewhat cost a material amount of supplies (I think it was 400,000 or so landmines at Kursk, although that's off the top of my head, I could be out by a fair factor there).
I agree that there's a decent argument to be made for leaving out an extended dig-in mechanic that would reflect landmines as too onerous for the players (much like divisional commanders and the OOB, although unlike divisional commanders and the OOB, it's not just an immersion thing), but not on the grounds they didn't have a strategic impact, or that they didn't affect different battles to a different degree.
If there weren't landmines, maybe the Axis might have forced a draw instead of a loss at Kursk, and the 8th Army might have got to Tripoli sooner and perhaps even forestalled a lot of the Axis build-up in Tunisia (which, ironically, would have been to the Axis' advantage, not losing nearly a quarter of a million prisoners and all that). Of course, landmines alone didn't turn the conflict, but then no single factor did, not even atomic weapons, so that's no argument for not including them.