@Carlo D. it's not necessarily true that most RE investors look for a CoC of 7-10%. As with most things in REI, it all depends on a myriad of other factors--things like the grade of the property, the grade of the neighborhood, the investment strategy, the investor's net worth and experience level, the investor's goals, the difficulty or ease of managing the property, vacancy projections, etc., etc., etc. ...depending on these types of factors, a 7-10% COC might be a grand slam success, or a train wreck.
A 7-10% COC (after PM fees and all other expenses) on an A grade truly turn-key property in an appreciating area with a huge tenant pool might be enticing (and probably doesn't exist in today's market). But, 7-10% for a C grade property that no PM wants to manage because it's a magnet for crime, non-paying tenants, vacancy, evictions, and repairs? No thanks--wouldn't touch that with a ten foot pole.
A property can look GREAT on a spreadsheet (with a high COC, high cashflow, etc.), and it can still be a complete nightmare that can ruin your life (indeed, we see no shortage of beginners in the forums who talk about buying a property that looked GREAT on the spreadsheet, but which turned into a total disaster). ...and the opposite is also true--some properties look mediocre on a spreadsheet, but can be excellent investments for any number of reasons (e.g.; tax benefits, construction quality, tenant pool, value-add opportunities, ease of management, etc., etc.). This is what makes REI interesting, in my opinion--it requires the investor to understand so much more than just the numbers on the spreadsheet.
But, to answer your question: yes, I would run the numbers for COC when purchasing a property in cash. I would also run a LOT more numbers, and do a thorough cost / benefit analysis looking at numerous factors like what I described above. COC is just one of many factors to consider when investing in real estate, and simply hitting a specific COC number isn't necessarily the ultimate deciding factor in whether to buy a property.
Good luck out there!