For the longevity of the game main issue here would be that the market is full of player-owned planes that have expired heavy checks. So they are of no use for new players which is my main concern.
It would be a bit wrong to force players to keep the checks up-to-date but some other elegant solution to encourage for it would be nice. Market broker declining to put the plane up for sale listings if there are already several similar ones with expired checks and this has them too? Or a bonus for paid by the broker if the checks are ok and plane is sold/leased? Or capping max allowed price for the plane with expired checks? ...or something.
For the topic, storage fee would be imposed as a "ramp fee" / "parking fee". Doesn't have to be relative to your base airport capacity as you can ferry them to the nearby ex-military airfield dump but they also charge you a bit to park the crap there until some unlucky guy buys it.. Overall, would be rather small and comparable to insurance fee.
So, if you're looking for an elegant solution, let's consider the following -
1. Add a filter to the used aircraft market to:
a. Only show Broker, Only show player or Show All listed A/C
b. Hide Aircraft with expired checks (or with checks expiring in the next 3 months as an option).
2. Implement the "storage" ability (I believe this is a longstanding feature request) for airlines to park planes without auto c/d checking them (this alone would eliminate the need for fleet transition frames to end up on the market).
Of course, on the already [-]'ed wish list:
1. Cycle/flight hour based MX - the C/D check clock isn't necessarily ticking as fast on parked planes