In my opinion it's a horrible idea.

When an account is compromised with 4 week powerdown worst case scenario if it's recovered on day 28+ all its stake whether it's powered up or not are stolen (Is it even worth recovering anymore?). Even if its recovered day 7+ after it's stolen it loses at least 25% of its powered up stake while with our current powerdown period at worst case when it's recovered on day 28+ it only loses 4/13 of its powered up stake, a little more than 30%. After 30 days of course you lose the account to the hacker on both cases.
Shortening powerdown is also bad because how our hardfork works. 4 weeks is not too bad (still worse than 13 weeks), but 1 week is plain horrible. If it's only 1 week exchanges will undoubtedly start voting for witnesses. You say our powerdown period is too long compared to EOS but they are having a huge governance problem. Even Dan Larimer is proposing staking pools with up to 10 years(!) lockup period and the 3 day lockup EOS tokens have 0 vote for BPs, the minimum lockup to have any vote for BPs is 3 month, pretty close with Steem right now and it seems like it won't have gradual weekly powerdown like Steem has. If an "investor" can't even commit to their "investment" for 13 weeks do they even can be counted as "invested" in the chain? If they just want to speculate on STEEM price that's what liquid STEEM is for, hold those instead.
The instant powerdown with burn fee is even more horrible idea. Now instead of losing 25% of your powered up stake each week when your account is compromised you lose 100% right away, GG!
However, I agree that in order to participate in PoB someone shouldn't be forced to lock up their capital for 13 weeks.

Here are my proposed changes instead:

• 2 separate staking pools
• The first pool has 1 week powerdown (even better than 1 month) and the second pool has 13 weeks powerdown
• Entitlements of the first pool: VP and RC
• Entitlements of the second pool: VP, RC, Witness vote, SPS vote, etc. (The benefits of SP right now).
• Delegations works as if the pools are mixed. (You can delegate 210 STEEM away if you have 100 STEEM staked on the first pool and 110 STEEM staked on the second pool). Delegations delegate VP and RC like how it works right now and will interact with the RC delegation pool however it works in the next hardfork.
• SP reward on posts can go to first pool or the second according to witness consensus. The name of each pool should be discussed with the community (only one of them keeps the name SP).
• Stake on first pool can be converted to the second pool instantly but not the other way around (similar to Dan Larimer's proposal).
• Current SP can be converted to first pool or the second pool on hardfork according to witness consensus. Each has their benefits and drawbacks. If it's converted to the first pool non-committed people gets weeded out really fast as they won't be converting their stake into the second pool but witness votes basically reset to zero and may cause instability in governance and block production for a short term. Converting to second pool is safer but will take 13 week correction time until it shows the results of the previous way. Of course we can assign a ratio too (like 90% goes to the first pool and 10% goes to the second pool) and have the benefits of both but needs a little longer implementation time.
• When these separate pools is implemented I think making the second pool powerdown period even longer than 13 week can be considered if we want to see more committed witness voters and more protection when an account is compromised.

Yes, these changes will be complicated to code but I think this is the way to go instead of simply reducing the powerdown period to please the so-called "investors" which in my opinion is very shortsighted .

That's my thoughts on this.