Border Guard:
If there is a Witch but no card that discards anything, Faithful Hound is strictly worse than Moat, so I don't think it means much if a card is strictly worse than another if its Reaction can't trigger.
Difference is, Moat and Faithful Hound still have the same on-play effects.
You said Border Patrol is strictly worse than Dungeon without its Reaction.
There is two ways to understand this:
The literal interpretation where you just pretend that the Reaction wasn't on the card, as you are doing for Faithful Hound and Moat. That interpretation is talking about a hypothetical which isn't the case, as the card DOES have the Reaction. It's factually true, but inconsequential.
Or you talk about the Reaction not triggering, in which case my point still stands. Faithful Hound and Moat have different triggers, a game may feature only one, in which case one card is strictly better than the other, or feature both to varying degrees, where neither is strictly better, or may feature none, where they are identical. A game may not feature Boarder Patrol's trigger, making it strictly worse than Dungeon, or may feature it, making neither strictly better.
Is your point that if there can be games where Border Patrol is strictly worse than Dungeon, there should be games where they are strictly the same? Or that there must be games where Border Patrol is striclty better? Why?
I'm not even saying that Border Patrol couldn't use a buff, you may very well be right about that.
Basically all I'm trying to say is that Border Patrol is laughably weak compared to Dungeon, which costs the same. Getting the effect now and next turn is huge compared to a Reaction that helps your opponents as much as it helps you. As I said in my last comment, Border Patrol is to Dungeon as Moat is to Wharf (approximately), except
even worse because the Reaction is strictly worse than that of Moat!
Moat and Faithful Hound having boards where one is strictly better than the other is fine because
their effects are actually somewhat close. Moat and Faithful Hound have the exact same on-play effects. A game with no Attacks leads to Border Patrol looking like a complete joke next to Dungeon, but the same can rarely be said of boards with ways to discard Faithful Hound but no Attacks or vice-versa. The fact that the Reaction even helps your opponents instead of just you means that it's really weak even in games that DO have Attacks.
It's fine for it to be strictly worse than Dungeon with no Attacks on the board, but if it's going to be so much worse than Dungeon with no Attacks, it ought to have a waaayyy better Reaction than protecting yourself at the cost of needing to have a Border Patrol while giving that same protection to your opponents for free.
Also, you pointed out an issue with it yourself, namely that the Reaction ceases to be strictly worse than Moat's in 1v1 games. That means its already low powerlevel drops by a not-insignificant amount as soon as you add a 3rd player. Card power levels shouldn't scale that poorly with player count.