Is" third seat, favorable vulnerabilty" the only appropriate time to pre-empt with "any seven" of a suit?
To answer your specific question: Other than third-seat favourable vulnerability, only when you are specifically interested in a small short-term bump in your results against weak club competition, and are willing to sacrifice your overall partnership rapport and skill level in order to do so.

Your argument is extremely faulty. If one is allowed to open 3 in a suit with a hand like such as

x-xxxxxxx-xx-xxx


then one is effectively removing the capability to open 3 in a suit with a constructive hand such as

x-KJTxxxx-xx-KTx


because it is too dangerous for partner to respond on the possibility of the second hand and risk going down 1700 or 2000 if you only have the first.

Further, you  are neglecting the value of the distributional information that you are giving to the opponents, and that you are depriving both yourself and partner of (from hearing an informative opponent auction) in making an informed opening lead and sound defence. Destructive agreements like this are discouraged by all authorities because they both prey on weak players, who do not have the experience and agreements to deal with them, and convert expert contests into extreme games of chance from ones of skill.

Yes, in a club game you will undoubtedly do well with such an agreement against weak players; but you will at best break even in the same games using it against experienced partnerships; turn friends into enemies; and see your tournament results plummet as you develop a reliance on such gimmicks for good results at the expense of sound bidding and play.

as I noted in a comment above:


  Yes, bridge clubs around the world have numerous fools who would bid thus - .... Bidding on the assumption that LHO received a defective bidding box, without any red cards, is lunatic bridge. LHO's bidding box is just fine, and [if an experienced player] he knows exactly how to pull that red card, whether it be for penalty or takeout.


Update:

It is also important to note that a very weak hand is much less likely than a merely weak hand. Thus that holding a hand similar to x-KJTxxxx-xx-KTx is much more likely than holding one similar to x-xxxxxxx-xx-xxx. Are you really sure you wish to handicap all the hands where you hold the former, just so that you can bid on the very rare occurrence of the latter?



Similarly one moderate feature outside the suit is much more likely than no moderate feature outside the suit, compounding the unfavourable statistics.

Update An example of how a system that encourages light openings enables opposing declarers to make contracts unlikely to be made otherwise.