Well, as always they will want to boil the frog slowly, so there will be multiple steps:
1. Gather information about foreign assets. E.g. the EU will force other countries to report assets within their jurisdictions from EU citizens. This is already (partially) implemented through agreements like CRS.
2. The EU countries will introduce new rules (under the “global tax avoidance” theme) that you will have to declare your assets in low tax / zero tax jurisdictions, but they are not taxed yet.
3. EU countries will get the right to tax income︀ and capital gains of their citizens that has a source in non DTA countries.
My prediction is that the days of paying zero income tax are counted for most people.︁ In the future you will only be able to avoid income tax if you live︂ on a small, isolated island like Bahamas, Cayman Islands or Vanuatu and live off your︃ savings.
As soon as you’ll invest in the main economies (US / EU / China)︄ the capital gains and all work related income anyway will have a withholding tax applied.︅
So even if your island technically has no income tax you’ll still pay because the︆ US / EU stocks, ETFs, bonds etc. that you buy will all apply a withholding︇ tax at source.