This is actually an economic issue, not a cryptographic one.
Suppose hypothetically that I'm mining, and I'm making a good healthy profit. I'm naturally going to keep adding more and more computers, to get more and more profit. But of course, the cryptocurrency can't let me expand forever, because it can't afford to pay me an infinite amount. It has to lower its payout, to get me to stop gobbling up more and more profit. I'll finally stop expanding when the cryptocurrency lowers my profit margins to almost nothing.
But, if my profit margins are tiny, then everyone else's are too. Then that means there's no room for inefficiency. Anybody who's in a place where electricity is expensive, or where they have to pay for cooling, or where land to build a datacenter is expensive, is not going to be able to make money.
That's why it's rough for home miners to make any money: a home-based mining operation generally isn't as efficient as a carefully optimized datacenter.
However, home-based miners have one advantage: they usually already have a computer that's already paid for, and whose cost can be considered "free" considering that the computer would probably have been doing nothing otherwise.
Memory-based proof of works don't change the basic economic reality that profit margins are going to be super-tight. But they do make it possible to leverage that "free" computer to get a slightly higher return, insofar as the cost of the computer was a meaningful part of the cost to begin with.
Unfortunately, in my opinion, memory-based proof of works have a flaw: they make it possible to hire a conventional datacenter (say, an Amazon EC2 datacenter) and use it for mining. That makes it inexpensive to temporarily bring a lot of hashpower online for use in attacks.
For instance, imagine that I had a cryptocurrency with 100,000 nodes, each with a single powerful CPU doing mining. How much does it cost to rent 101,000 powerful CPUs for an hour, to do a 51% attack? Answer: a few million dollars. Very much within the reach of any significant organization. You couldn't launch a 51% attack against an ASIC-based cryptocurrency for anywhere near that price.
I'm not honestly sure how big a risk 51% attacks are: I'm not sure many people are actually motivated to do that.