OK, let me offer some more detailed ideas.
The concept of reducing opponents potential is a little tricky and we usualy tend to view it from our percpetive of winning and leaving opponent unable to counterattack, but that is not the full story, because losing the battle will lead to a reduction of our own potential as well. When a number of 4 vs 3 attacks take place on the board, BOTH players' potential is reduced, the map will simplify to regions with 2s instead of 3s. It is just that the attacker has some small advantage in those battles, he will, in a large scale lose 10 troops and kill 11 for example (random numbers) For the moment, lets simplify the discussion by ignoring the profit from winning 2-0, followed by a superior in odds 4-1 attack, because in our example, we already have a 1 to attack anyway and we discuss if it is a good idea to choose to ignore it. This means that the concept of reducing potential is not that great as we may sometimes think. If you deploy 7-8 4s around the board and you do not make any attack with them, you have of course played wrong, but you have not blundered so much as you may think. Probably just 1 troop. I do not say that this troop is not important, but the chances that your attacks will succeed and reduce the opponent's potential are not much greater than the chances you fail similarly and reduce your own potential and weaken your boardering regions. The attacker's advantage in 4vs3 is important, not only because of his superior chances, but also for the chances to simplify the battle to a 4-1 roll. That case offers you an extra 0.32 troop during your next assault click.
In general, a 4-1 assault has an expected profit of 0.32 troops, a 3-1 has an expected profit of 0.16 troops and a 4vs 2 single click, single assault,(not to the end) has an expected profit 0.16 as well. (the attacker's advantage is half that, but we are talking about 2 battles)
Now, let's move to the case discussed here, where you have a 4 boardering a 3 and a 1 and let's compare the senarios. What you mathematicaly suggest, is that you do not want to cash in that 0.32 troop that is already available to you by attacking the 1, prefering to gamble to drop both regions to 1s, followed by attacking 4-1 and if things go well, 3-1 as well.
This in turn implies that the board situation demands making 3-1 attacks. If the board situation does not demand 3-1 attacks, then there is no discussion, the concept is obviously wrong.
1) My suggestion, attacking the 1 is the simple case, you win 0.32 troop. By clicking the button "assault" against the 1, you statisticaly win 0.32 troop, no more, no less. We also have to add the profit from followin up with a 3-1 attack in case we lose, because assumption is that those attacks are favourable and must be made. Losing 4-1 at first roll is 34% and the profit from a 3-1 assault is 0.16 troops. This makes 0.16*0.34=0.05 troops. So, my suggestion ends in winning 0.37 troops
2) If you attack 4-3 clicking once, what will you gain? The answer is 0.16 troop at first roll. Here, we need to add the improved odds in case you reduce it to a favourable 4-1 attack. Chances to win 2-0 are 37%, in that case you make a 4-1 assault, winning an additional 37% multiplied to 0.32, equal to 0.12 troops. Total 0.28 troops.
So, in senarios that the board demands making 3-1 attacks (otherwise there is no discussion and nothing to talk about), the suggested tactic has the advantage of having a chance to kill the sole 1 as well, after winning 2-0 in 4 vs 3, followed by a succesful assault on the remaining 1. Chances to win 3-0 are about 25%. So, in 25% of the cases, you will follow with a 3-1 attack, which offers you the gain of 0.16 troops. 25% multiplied to 0.16, equals 0.04 troops. The original 0.28, added to this 0.04, equals 0.32 troops.
Also, first tactic has 85% chances to conquer a region and second tactic has 14% chances to conquer 2 regions, 49% chances to conquer none and 37% chances to win one , for a statistical sum of +0.65 regions. This makes the assumption that after a 1-1 result, player will switch to the 3-1 assault of course.
Also, in first plan, I have 66% chances to end up with a stack of 3 for next round assault's and 33% ending with a 2, while second plan ends up with a stack of 2 in all senarios
PLAN A +0.37 troops, +0.85 regions and a remaining stack of 2.66 troops for next round's assaults
PLAN B +0.32 troops, +0.65 regions and a remaining stack of 2 troops for next rounds assaults
Each time you use this tactic, you lose 0.05 troops, 0.2 regions and 0.66 troops from next round's stack and so, you should not use this, unless there is a very good reason to do so.
In fact, to be honest, I am surprised that the numbers are so close, I had the impression that this tactic would have been wrong even if opponent had 13 regions, but this does not seem to be the case, unless I made some mistake. In this case, you have a 14% chance to break him down to 11 regions, for an extra gain of 0.14 troops. This offers plan B a lead in troop count by 0.09 troops, although the 2 other disadvantages in expected regions and remaining stack size remain. This is a debatable situation I think and I will describe it as unclear decision, depending on more detailed factors of the specific game.
CONCLUSION. Suggested idea seems wrong to me in most cases and debatable only in case the specific situation favors the execution of 3-1 attacks and opponent has 3n+1 regions, n>3