I didn’t see any limit to the number of people you can challenge: OGS Ladders · online-go/online-go.com Wiki · GitHub
I think it needs to be updated in more than one place so 
Your argument would work if things were absolute, where players at position 2-10 will either always follow the strategy of not challenging the player at position 1, or never follow that strategy.
But that’s not how it works in practice.
In practice it’s a matter of incentives. A player in a lower position can challenge the player at position 1, or not.
Now, imagine you’re player 2. You’ve challenged player 1 once or twice in the past, and lost. You have been challenged and have challenged players 3-10 in the past, and sometimes won and sometimes lost.
Currently you’re at position 2. You’re hesitating on whether to challenge player 1 or not. On the one hand, you have a bit of fighting spirit and wants to try again to defeat player 1 and reach first place. On the other hand, player 1 has already defeated you every time you’ve challenged them in the past, and you’re a bit hesitant to try again and risk losing again. Then you notice that no one has challenged player 1 in some time. Thanks to the new timeout policy, you now have an extra incentive not to challenge them, and wait for them to be kicked out.
Players 3-10 will likely keep challenging you anyway, whether you’re at position 2 or at position 1, because they know they do beat you sometimes. But they’re hesitant to challenge the current player 1, for the same reason that you are.
So then if the timeout rule never applies to player 1 in the ladder like
how does that change the situation? There’s no way to remove player 1 without beating them, unless they go inactive and you time them out the same way you can in the current system.
Does the same logic apply now to player 2? Everyone will refuse to challenge player 2? But player 2 can always challenge player 1 to stay in the ladder, even if they can’t beat them. They’ve no way to oust them anyway
(I would probably also word it that being challenged excludes you from the timeout also - some people are happy to sit where they are and be challenged I believe - I suppose the timeout rule might annoy them if they haven’t challenged or been challenged in a year)
With my proposition, player 2 has an incentive to play at least 1 game/year against player 1 in order to stay in the ladder. And player 3 needs to challenge either player 1 or 2 at least once a year to stay in the ladder, etc.
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I guess the point would be that if it doesn’t significantly change whatever the meta game is at the top of the ladder, and it means that the ladder looks more like the top 200 (where most people have 1 or more games going) than toward the bottom thousand or so, where there’s gaps of 30+ players with nobody playing any games, it’s probably not terrible is it?
Unless one wants an easy path to jump up places with timeouts.