The ancestral solution to oxygen transport is with hemoglobin (or, similar proteins) dissolved in blood (or, "hemolymph", but, basically, dissolved in water. ) What was the advantage of enclosing the oxygen-transport proteins in cells?
If you enclose the globin in a cell you can achieve a high concentration of the globin, which makes for a faster, readily usable pool available, and it is not subject to degradation (via proteases, or other mechanisms) as if it was just dissolved. In addition, all other functions of the globins (pH regulation, CO2 metabolism, etc) will be more tightly controlled if the globin is on the same site (i.e., inside a cell), instead of being mixed in a milieu. All of that has probably more to do with the evolution of the entire circulatory system, as a whole, and only sequentially as the 'enclosure' of globins in specialized cells. You can find some more details here.