As a default mode, IF that rubber hose was supposed to catch the condensate due to a leaking case gasket (which was common on those cases, best I can tell) AND/OR the car had solid vinyl factory floor mats in the front floor areas, the carpet and pad could be damp and you not know it. I discovered this on my '70 Monaco after I'd had it for a while. I took the rh floor mat out and it was damp on its back, as was the carpet.
After I got to looking at things, the case gasket is something like an open-cell rubber, which is fine. The case halves are held together by slip-on clips and screws. All sounds normal so far. But the rubber has enough surface tension (on its sealing surfaces) such that there is a gap on each side of the clips, from which condensate CAN escape (rather than going out the drain tube). The old-line Chrysler service manager claimed, too, that they stopped using a drain pan under the evap core, so that the condensate went directly to the bottom of the case and then out the drain. Those gaps by the clips gave it another route "out", it seems. Hence, the split heater hose contraption you have.
There CAN be a better way to keep the hvac box halves together, I suspect. Like using prevailing-torque flange-head nuts (with a floating captive washer, possibly) rather than the slip-on nuts the factory used. Plus putting a skin-coat of black silicone sealer on all sides of the gasket prior to installation, installing it after it cures a day or so.
Additionally, in some humid environments, the outside of the hvac case CAN sweat, with that moisture falling on the floor beneath the case.
I concur with the "use it until it leaks" orientation for the heater core. When you are flushing it, flush it in the normal direction of water flow through it (which is in the heater hose routing image in the FSM, usually. I was flushing the core on my '67 Newport, getting a clear flow out of it, THEN I decided to do the "reverse flush" operation, which then sent things backward and plugged the core. Whoops! And it's still that way, years later.
In the mean time, DO shop around for a quality heater core and evaporator core from a good vendor! Sooner or later, you'll need one or both.
Just some thoughts and observations,
CBODY67
