and they will start arguing again how long(or unnecessary) the 4 weeks power down is by comparing to EOS or other blockchains with only a few days.
That is exactly the problem. Most people who disagree with 13 weeks, will most likely also disagree with 4 weeks, even though it might be the better evil.
But 13 weeks isn't ultimately bad, it only becomes bad when the incentives aren't there. IMO, it makes more sense, to implement incentives for longer power-down-time, instead of removing it altogether.
Similar to your 2nd method, there could also be incentives for increased powerdown time: (rough example numbers)
| Rewards | Staking Duration |
|---|---|
| 2% p.a | 1 week |
| 4% p.a | 1 month |
| 8% p.a | 3 months |
| 14% p.a | 6 months |
| 20% p.a | 1 year |
!BEER
Interest rates have been shit for banks for a long time, but there's a concept called a CD ladder, where you have a wide range of CDs with different maturities/rates. This way you regularly have a CD maturing and liquid cash available. I could see laddering my power-ups in the same way if a choice were given.