No team in a position to make the playoffs has ever traded a star incumbent starter without a highly drafted future star 1B already outperforming them and taking their starts. If Demko does that, then it would make sense. Otherwise there's no precedent for this happening, which would seem to undermine your description of it as common sense.
for context, three different situations in the early '90s with some level of comparability (i'll let you all decide how much in each case)—
1993 rangers. vanbiesbrouck is the former vezina winner, richter is the young hotshot. that was the year messier got roger neilson fired. going into the deadline there was a lot of talk of new york trading one of them because the expansion draft was coming that summer and teams could only protect one goalie. trade deadline was march 22, 1993. going into it the rangers were 33-28-11... not great but still in playoff position.
decision: they kept both goalies.
result: they went 1-11-0 the rest of the way and finished last in the wales conference. beezer played the first two games after the deadline, losing both. richter plays the next one, loses. then back to beezer, who gets a shutout. then he loses again, and corey hirsch(!) gets a game, which he loses. hirsch gets a second game, where he gets pulled, richter finishes that game and plays out the last five, losing them all. keenan was hired as their coach in the summer. before the expansion draft they traded beezer to us for doug lidster because we knew one of the expansion teams would pick him first, allowing us to keep our own backup, kay whitmore.
1993 leafs. fuhr is the former vezina winner/hall of famer, potvin is the young guy. up to february, fuhr has 29 games, potvin has 23 games. they both have good records but potvin's stats are way better.
decision: they trade fuhr to buffalo at the beginning of february for dave andreychuk and the first round pick that became kenny jonsson.
result: after potvin takes over, the leafs get really hot and go 20-9-4 to close out the year before making it to the third round, where they lose to LA.
1994 devils. chris terreri was the legit starter, he played between 48 and 53 games the previous three seasons and received stray vezina votes in two of those years. brodeur was a rookie.
decision: they kept both goalies but handed the team over to brodeur toward the end of the season. up to march, it was a fairly even split, with terreri getting a few more games most of the time.
result: brodeur started the playoffs, beating buffalo in the first round, but lost the first two games of the second round against boston so they went back to terreri, who won three in a row. brodeur got back in for game six, pitching a shutout. he started the rest of the way, losing in the wales finals to the rangers in game 7 double OT. terreri backed up brodeur full time the year after and the devils won their first cup. the rest is history.