No, any worker who's had a job will want to earn the bucks so he'll work regardless of the weather. If basers really want the gang rewards, they will be willing to wait till their cap has been lifted or pay the tax to base. Afterall, all gangs are basing for the rewards. If they give up just because of the tax, then too bad for them those who want it bad enough will get them.
As I have said it will not discourage any players from leaving the game because when we get those monopolist gangs out, basing is much easier for newer or weaker gangs. It is in effect deregulating the system so we have the competitiveness up. If any player feels discouraged by the tax, then by all means they are free to stop basing - considering that taxes apply to gangs with thousands of hours, only members from those gangs would be likely to be "discouraged". But we need to weigh this against the fact that their gangs have already had thousands of hours and it's likely that basing is habitual, so even if they are discouraged, they are not likely to stop basing because if I am 500 hours closer to getting a gang hideout, why would I stop basing just because of the tax? The basers will likely wait for the cap to be lifted to continue basing, or pay the tax to base if they are rich enough.
But since everyone likes to use the slippery slope argument against this, then let's say those in the gangs with thousands of hours really felt so discouraged, they have low level of perseverance and resilience, and they really stop basing, then it will be good because that's one less monopolist gangs out of the way for weaker gangs to replace them. But as established, this is not likely because basing would be habitual and no one will want their thousands of hours amassed thus far to go to waste if they don't get the most rewards out of it.
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Read above and also, know that taxation is a interventionist approach, so it is natural that it'll draw opposition. Just like nerfing guns is an interventionist measure, this too is one.