If I consider the likelihood that nobody will have any inf at all - and will all be starting from scratch - it will take quite a bit of time for one of those special PvP IO enhancers to reach the pre-closure asking price of 1-2 billion inf.
A fellow like me - who labored to get to 100 Billion inf by games end (goal met! I converted it to prestige to make my SG #1, lol) - will restart with zero influence. Yeah, it'll take me a very long time. I think, and I could easily be off - that from level 1-50, not relying on income from the market, a character might earn about 20 million inf.
So, yeah, it will take "most" people a lot of time to earn enough to have any inflation effect. Honestly, I wouldn't worry about it.
If I get a purple - I'll likely be keeping most of them for the next characters I have - not selling them. Because of their rarity, unless they are sold in a store, it's going to take a long time to get a full set.
If memory serves - there was an enhancement changer type thing - I forget what it was called - or even how it was used - but that thing will be used a lot, if it's available.
I honestly wouldn't worry about inflation. Let the market deal with it. Just add a hero equivalent of the IRS. Inflation problem solved, we'd all be taxed on how much inf we earned. And, if we gave some away, we could get a reduction in our taxes. Just like real life!