In the US you can be an ATS(Alternative Trading System) or a full blown exchange. All dark pools are ATS's. This gives you a bit more leeway in terms of what you are allowed to do, ie hide orders, trade only at midpoint, trade only at certain volume's etc, even report trades in a slower fashion.
A full blown exchange has alot more scrutiny but comes with one huge caveat, all other exchanges must route orders to you if you have the NBBO(National Best Bid or Offer) as dictated by the SEC's REG NMS 611.
This means if an order to sell comes to the NYSE for 5.00 and takes out the entire first level forcing the NYSE to have a bid of 4.99 and there is still more volume in the order, the NYSE has to send the order to another exchange still showing $5.00 as its bid.
Since the exchanges make money when each share is traded they don't really like to do this( as a side note, this is how flash orders came about, exchanges "flashed the order to a select few market makers for 50 milliseconds before sending it to another exchange giving the market makers a chance to fill it, and keeping the commissions at the exchange, people got pissing about it and it no longer happens).
If IEX transitions from being a dark pool to an exchange this requirement to use their quote as part of the NBBO might mean more liquidity, and hence more profit, for them.
The issue with this is that IEX is the first proposed exchange, atleast to my knowledge, that has an intentional built in delay, meaning that its quotes are by design slow and stale as compared to the other US exchanges.
They are arguing to the SEC that since the NBBO is determined by the SIP(the system that aggregates all other exchanges quotes to determine what the NBBO is), which itself is slow, that this doesn't really matter much.
On the other side of the debate is a literal whose who of the finance world, not just HFT's, arguing the slipper slope defense, ala well if they delay 350 microseconds, what's to stop someone from having a 2 second delay or 1 day delay in showing quote.
I don't really have a dog in this fight but most people I know believe that IEX is going to lose this fight, though there is a loud contingent at the SEC itself that wants IEX to win to act as a test case for what the SEC can do to shape the market microsructure of the US cash equity markets.
As to becoming a place to list your company, I think Levin is right here... no one cares at all what exchange the company is listed on, even the company itself.
EDIT replaced ECN with ATS above