The very legitimate concern is that if any of your tables were purchased through the TPA app and not say through Steam, you need to log in to play, otherwise it will show those tables as being locked. Same goes for people that contributed to a Kickstarter or won the tables through a FarSight giveaway. In every case, you need to first log in to the FarSight servers in order to have access to those tables. FarSight has said that keeping those servers open in very inexpensive and as long as their doors are open, so will the servers. That's one of the key benefits to buying the Arcooda stand alone pack, it is entirely self contained and won't be vulnerable to updates nor does it require a log in. Arcooda actually has these still available for sale (they did a block purchase so are legally still able to offer these) if it really is a concern to someone.
Not only am I not concerned, I'll progressively get less concerned as tables release for FX3.
I've had this exact problem recently and I am very worried for the future. I attempted to change my password for my FS account and I was stuck in an endless loop of "password not verified use forgot password to verify" Only the forgot password system doesn't send a verification only the reset pass so I was unable to log in on any platform. Because of this I lost access to 50 of my tables on steam as I bought those through the app and not the steam store. After discussing with farsight they had to manually change my password and said in the future to use the website not the app to reset. However this doesnt work either. Even though the apps accept the password they had to create for me, the website will always return the same error of "password not verified use forgot password to verify" Speaking to them they have no idea what is causing that and they sent it to their internal tech support. That was a month ago and still no results. If and when FS closes the doors on TPA there's a more than likely chance many will lose access to tables on steam because of this issue.