I have a way of cooking cod loin which has never failed me before.  This time, large parts of each loin became so rubbery as to be unchewable.  I know several things that deviated from my usual recipe, but I'm wondering which thing was the culprit. First, the recipe:  Cod is dipped in milk and egg and then rolled in panko mixed with Cajun spices.  A little olive oil is heated in a cast iron skillet.  Cod is fried for a couple minutes on each side.  Then the heat is turned to low and the lid is put on the skillet.  The fish "bakes" in the cast iron for about 11 minutes.  This has never failed to give me nice white flaky cod. A couple things were different this time:  These were from a bag of frozen cod loins (maybe from Sam's Club or HEB.)  These were the last two, so they'd been in the freezer a while. I had gotten these last two out a couple weeks ago, and then didn't make the fish, so they went back into the freezer. Instead of 11 minutes, they got more like 20 minutes of "baking".  On the first piece of fish, I took a bite off the end and it was fine.  The next bite I couldn't cut with my fork.  It was almost exactly the texture of that triangular piece of cartilage one gets on a chicken breast: rubbery, tough, bleh. I would think that if over-baking were the problem, then the fish would have been tough at the ends, but the ends were the only edible bits.    If it were that Sam's Club just stocks bad fish, then I'm incredibly unlucky/lucky in that out of a bag of 15 pieces, I chose two at a time over the months and only the last two were bad.  That leaves "refreezing."  Only these two pieces were thawed and then refrozen.   Could that have caused the puck-ness? 
Your supposed advantages are not correct.  I believe if eggs are mixed too much, whites can get a rubber-like texture.  No, this is not correct. Are you thinking of gluten? That is the ingredient that gets tough with overmixing. So by that logic, you should be adding the flour last - but the whole point of recipes which are being held for a long time is to allow time for the starch in the flour to hydrate, and with the longer periods (you mention 24 hours), to allow for the building of slight sourdough flavors. So you cannot add flour last either - or you can, but then you don't need to keep the batter around. Anyhow, there is no change in toughness when you add eggs first.  Eggs are fresher when they are in their shell  They may be "fresher" by common sense understanding of the word, but by food safety rules, the two batters (the one with the eggs added before a rest, and the other with eggs after the rest) are equally safe. The food safety is not increased. On the other side, if your suggestion is followed, there may be some slight disadvantages in handling. They are not so terrible as to make your suggestion unworkable, but together with the lack of advantages, they provide a good reason for recipes preferring early mixing. A list of some of the disadvantages:  Not only is it more convenient to only get out a whisk once, but there are also people who prefer to mix the eggs with the flour first because this is their preferred method against getting lumps, There are the recipes which require you to start with an egg and then adjust the consistency with incremental additions of flour and milk There is the slight effect of possibly less-well beaten egg diffunding better into the mixture during the resting period. Basically, if you want to go to the trouble of doing a resting period, whose purpose it is to get everything to settle together, you'd better add everything before you rest it.  I must say that personally, I actually do add "egg last", but that's more of a side effect of my method. I use a very simple recipe (only eggs, flour and milk) measured by weight. I whisk by hand, and I have noticed that I get the least lumps when I first whisk the flour with the milk. This automatically means that the eggs (separately stirred, without whipping) come in last. I don't rest my batter, so there is no question of adding it after the rest (and if I did rest, I would add it before the rest). So you see, egg last is not impossible, just like Willeke said, it just has no special advantages, and in some cases it comes with disadvantages. 