Inefficient Markets

In the excerpt by Frank, he discusses the problem of commitment between two parties. In presenting the problem, he provides two examples that illustrate the general framework he is considering. Both of these problems assume inefficient markets, in which information and other logistical concerns ultimately prevail to prevent ideal choices (and matches) being made.
In the example of searching for an apartment, he says: "At that point, you know there is a better apartment out there somewhere, but your time is too valuable to justify looking further. You want to get on with your life."(6) This end result is because of his earlier assumption: "you cannot possibly inspect each of the thousands of vacant apartments." (5) In the second example, concerning the search for a mate, a similar problems sets the terms of his paper: "No matter what your mate's vision of the ideal partner may be, you know there's someone out there who comes closer to that ideal than you."(7)
It is this critical assumption that informs the rest of his framework, which I think goes something as follows (I may be wrong, please feel free to correct/improve):

1. Imperfect information and logistical limitations limit the market and result in non-ideal matches/pairings (commitment problem)
2. Therefore players must make a cost-benefit analysis and settle for some non-deal pairing they deem good enough 
3. Players then need to find means of creating stability within non-ideal pairings to mitigate the risk of finding a better pairing (commitment device)

My question concerns the first step in this logic. What if you were able to overcome the information problem and create a perfectly efficient market? This may already be the case thanks to the internet and information sharing protocols that facilitate the diffusion of big data, but the point stands regardless of this empirical question. 

If a market was perfectly efficient (i.e. there was perfect information on behalf of all parties) would this invalidate the entire problem? If I could easily find and match with my ideal partner, it seems to me that we would not require any additional commitment devices. We would both know that we were with our ideal partners, so there would be no risk of finding someone better or generally doubting our relationship. In the case of an apartment this would also apply, as I would simply be content with my ideal apartment, knowing there's nothing better out there. 

That being said, would this even be possible? My guess is that it might be possible in the case of apartments or other such clearly definable goods, but not with something as organic as a partner.