Expanding on that, another good way to get off of the top platform if you went up there to try and force them to come to you is to SH or FJ and then FF through the platform. This is a pretty good way to get down to because you have a good degree of control of how far in one direction you can go because you can do things like SH backwards before the fast fall and use the backwards jump momentum to go further in that direction.
As far as dealing with Falco's hiding under platforms and shooting lasers (aka what 90% of mid level Falco's are gonna do) there's a couple of things that you could do to deal with it.
You can run directly at him and force him to respond to you. This is obviously better if you can Powershield well, but it isn't absolutely necessary. Try to pay attention at which distance relative to you the Falco likes to move and how he likes to move.
If he doesn't move out from under the platform when you get close enough to jump on it they you have a nice mixup situation set for him where you can either FJ at him and either land on the platform, or you could FJ at him and FF through the platform with either an aerial or no aerial so you can maintain pressure up close to him. Ideally you'll want to wait until he shoots a laser before jumping to or through the platform so you can get closer to him as he's committed to the laser. From here, standing on the side platform is a pretty god position to be in as long as you aren't directly in the path of Falco's FJ because this means that he can't easily jump shine you. If he tries to get into a position to do so, you can do something like SH and FF through the platform and bair him as he tries to get in position or you could do a shai drop nair at him. If he tries to retreat further back then that's pretty good because you just made him give up space, while being in a very good position to prevent his forward movement so try to hold that position as well as you can. Another nice thing about standing on the side platform is that it's easier to catch Falco's that like to FJ out of situations where they're cornered which can be really annoying to deal with.
Overall, I think that jumping to the side platform that Falco is hiding under is a really good move as long as it doesn't put you in a position to be easily shined because you get to keep a lot of your options open while being a direct threat to Falco. If you can't really get on to the platform with out putting yourself in a position where you can A) avoid getting shined easily or B) avoid giving up your stage control (i.e. staying in front of him) this is a good place to do the FJ fastfall trough the platform to hit him in the same manner that you'd do a FJ aerial over the laser as if the platform wasn't there. If you're gonna do this make sure you can do stuff like FJ, FF through the platform, and still get a nair out. Depending on which stage it is, this can either be no big deal, or surprisingly difficult because the lower the platform is, the faster you have to let go of the control stick from the FF to get a nair out.
Ultimately the way I think it should play out is, if they're hiding deep under the platform, then Fox gets to jump on the platform with relatively little risk and from there he can hold that position extremely well and he as a lot of ways to convert that position into hits. On the other hand, if Falco is in a more shallow position under the platform then he doesn't really get the added benefit of hiding under the platform because you can sort of treat it like it isn't there by doing stuff like rainbow nairs or drills like you would on a stage like FD.
One of the ways that Falco likes to deal with you jumping to side platforms to deal with him hiding under them is to shoot high lasers to stop your FJ. This can get really annoying to deal with if you aren't used to looking for them, but once you do get used to seeing it you should start mixing in running under the high lasers as he SHs if you see him try to go for them. From this you can either grab him or go for a running shine to score a knockdown and pressure depending on how close you were to him initially.
Also, if you don't feel like dealing with this whole scenario in the first place, you can jump on to the top platform and see if that will force them to try and interact with you since Falco has a hard time trying to hit someone on the top platform. From here you can either try to hit him as he's trying to hit you, or, if you don't want to risk that going south, focus on getting yourself off of the platform and forcing things to go back to neutral so you can hit Falco before he can get under a platform again. As a bonus, if Falco doesn't really want to engage you while you're on the top platform, you can go from the top platform to the side platform that he's hiding under very safely so you can easily transition to the stuff I was talking about a few paragraphs up if the situation calls for it.