I believe, unfortunately, it's necessary to reference real life signalling and ask, what real life signalling system are you emulating? Because "operate properly in one direction" really has dozens of different implementations on different railroads, in different countries. "Proper" ABS for example, has no fixed direction and just responds blindly to block occupancy (all signals permissive in the absence of trains). "Knock down" systems allow a centralized controller to set a direction for a series of blocks (all signals are usually restrictive in the absence of trains), lights will go green in one direction only, and "knock down" to red after the train has passed. Is that the one you mean? I'm confused about your example because if trains meet on the same track, one faces a "stop and proceed" and the other faces a "stop", the result will still be a stall, even though no head on crash. Why ARE they trains on the same track in different directions? Are there turnouts in play that you haven't mentioned?
Are you familiar with the concept of an "interlocking"? This is, in its simplest form, a track junction where the signal aspect depends on factors above and beyond block occupancy. For example, a signalled turnout or diamond. A series of knock down mode ABS type signals terminates with an interlocking at each end; this is because it is where the stop that propogated all the way down the blocks, ends and other types of signalling begin (the point where the first set up "proceed" begins, and the place at the other end where the last set up block ends).
You say it "doesn't make sense" but what I am saying is, the sense depends a lot on the signalling conventions that you have decided to use.
The setting of a set of knock downs corresponds roughly to a train order. Generally, it would be actually paired with an actual train order, usually communicated on the radio these days. Never would a train trigger a knock down series of blocks automatically just by entering the first block. That is an executive function of the Railroad Traffic Controller. To imagine why this might not work, consider what might happen if two trains entered the block sequence from both ends at the same time.
Another subtlety of knock down blocks - in some but not all systems, if the destination (after last) block is occupied, the circuit is prevented from setting up "clear" signals all the way up to the origin - the departing train would see a "stop" at the departure point, because the destination interlocking is occupied. In other words, first signal mirrors the state of the final signal.