To the man with a hammer, everything looks like a nail.
The poster’s hammer seems to be kidney function. Mine is the biochemistry of the erythrocyte (red blood cell). Others, no doubt will be able to provide yet different perspectives.
From a biochemical point of view the erythrocyte has a limited repertoire of metabolic pathways compared with other tissues. However it does have an extremely active pentose phosphate pathway (not universally found in tissues) and the function of this is to provide the reducing cofactor NADPH, which is needed to maintain glutathione in a reduced state. The importance of reduced glutathione in these oxygen-carrying cells is that it provides protection against reactive oxygen species — something that could not be done — or at least not controlled so well — in the blood plasma.
Another feature of haemoglobin is that the equilibrium between the oxy- and deoxy- forms involves the small triose molecule, 2,3-bisphophoglycerate. This is described in the answer to another question. The ability of the erythrocyte to synthesize this molecule allows the sophistication of this control.
I imagine there are many more examples. (Any added in comments will be added.)
One could argue that these metabolites are not indispensable for organisms (glucose phosphate dehydrogenase deficiency does cause haemolytic anaemia in man), and this presumably explains why the simpler organisms you mention (and about which I know little) can dispense with red cells.
But a question certainly worth asking.