In Bitcoin, we always have better, more power efficient ASICs. The miner who is first to install a new ASIC, obtains temporary advantage over other miners (assuming all other variables equal). A new ASIC basically redistributes the constant flow of wealth (25BTC/block) among miners, ordinary users don't care.
In Iota, I'm afraid, it'll be profitable to use ASICs against users. If minimal PoW per transaction is small enough then a small battery of ASICs might be enough to outPoW the whole legitimate network armed with CPU PoW.
Bitcoin has constant PoW during a week too, I don't see how constant PoW leads to an insecure state. Would anyone create ASICs for Bitcoin mining if there was no subsidy (25 BTC) nor transaction fees?
Security of Iota relies on assumption that an adversary controls less than 50% of hashing power. This is a standard assumption in cryptoindustry. Bootstrapping period will be protected by checkpoints.
So you allow to duplicate a transaction as long as PoW is also duplicated.
What about attempts to rewrite history by rewriting the envelopes?
In this example from the whitepaper, if I wanted to censor envelope F and the corresponding transaction (because e.g. it contained a spend that I want to roll back), could I "route around" it by spending some electricity and rewriting references in envelopes of E and B so that they no longer point to F but somewhere else? Then there are no references to F in the graph any more, I can safely delete it and share my version of the history with other nodes. How will they know which history is right?
The history with the heaviest tangle is right. To rewrite the history you need to control most of the hashing power.