Exactly, nobody is going climb something vaguely equivalent to 4 stories under a hot sun just to get back up to their car...they'll continue to park on sidewalks instead.
This proposal is a phenomenally stupid idea and will most likely gain zero traction. Without even touching the ecological concerns, it's foolish to build more parking because it simply begets more cars (and thus the need for more parking). It never ends.
Admittedly, Gustavia is becoming extremely congested. But this is indicative of a transit problem, not a parking problem. There is simply too many cars on the island (likely more autos than residents at this point).
Better solutions to conquering the congestion of Gustavia would include:
-bus service: reliable & frequent routes between St Jean & Gustavia as well as loops reaching out to daily commuters living in places such as Colombier, Saline, Toiny, etc could probably reduce the number of cars needed on island by half, if not more.
-improvements in other forms of transit: the growing network of sidewalks is slowly making the island more friendly to walkers. Bike lanes might also help. Perhaps even some kind of light rail/cable car connecting St Jean (airport) & Gustavia over the hill. It could even be a tourist atraction in itself (think San Francisco). Possibly even water taxis could help people get around the island.
-moratorium on new automobiles: at a minimum, if someone wants to bring a new car to the island then they should have to send an old car off the island. There are already too many abandoned autos doing nothing but rotting. I'm not sure what the ideal maximum number of autos on the island would be but I would guess that it has already been exceeded.
-regulation & restriction of car ownership: perhaps one per household to encourage car-sharing. Certain businesses would be allowed to have auto but even those should be restricted. For example, construction companies could have trucks but not the large new types that are becoming more familiar here, rather only the smaller old fashioned models. Even for private cars, smaller size should be encouraged. Maybe additional import duties should apply to autos that exceed a certain size.
Freedom & independence are trademarks of islands like St Barth but (as much as it chafes me to admit this) St Barth could also benefit from some top-down, Disney style management of issues & systems like transit. Leaving it up to market forces has created a situation of increasing congestion, environmental degradation, car accidents and general aesthetic loss.
Unfortunately, rental car agencies & taxi drivers are entrenched local businesses that fight vigorously to protect their own interests at the expense of the island's greater well-being. Sadly, intelligence yields to local business interests. Provincialism at it's best!