For example, every month you and every other wallet would pay 20% of their bitcoin evenly to everybody else.
There is a technical issue with this, and a social issue:
Technical: How is it decided where the 20% gets paid to? How do we determine that each actual human being is being paid, and only being paid once? If you agree to centralize the control of this function, it isn't too tough: everyone just registers their identity with the central authority, so that the central authority is solely responsible for ensuring all payments are accurately made.
Of course, this is entirely antithetical to the design of bitcoin: there is no such hierarchy or position of authority in the network. Without the central authority, there is an obvious issue: a single human could just register many different address/devices/IP addresses/etc, to gain more than their 'fair share' of the redistribution**. This is a fundamental problem for decentalized systems, it is not trivial to solve.
Social: It will likely be difficult to convince people to opt into a system wherein they may lose up to 20% of their net worth every month. I think you can set this tax to whatever level and frequency you'd like, but it won't change the situation much.
The function of such a system would depend on the altruistic participation of the wealthy. This is not a stable proposition, we should expect that a wealthy and rational actor may not opt in to such a system, given the choice.
Would it incentivize more transactions and economic activity?
It would incentivize moving your wealth into a different financial instrument/money.
These two ideas, bitcoin and wealth re-distribution, are inherently incompatible. Bitcoin is entirely opt-in, whereas for wealth redistribution to really work, you need a system which does not allow the users to opt-out.
**Interestingly, bitcoin mining is itself a solution to this problem: users that want to gain the reward must prove that they have spent energy securing the network to do so. There is no way to fake the energy, and spending more energy does not win you a disproportionate amount of the reward. Bitcoin mining is a probabilistic solution to this problem of sybil-attacking the network: the attacker can no longer fake being a large number of nodes on the network, they must spend real resources to participate.
