As Lynda said, probably the biggest reason we don't add our haplogroups as tags is because tags are so limited, only 20 allowed.
But there's actually a more important reason, and that is because (in my opinion) haplogroup terminology has become rather ambiguous, especially the word 'haplogroup', and to be a useful tag would require some standardization. People often try to be more specific by adding the terms 'subclade', 'haplotype', and 'terminal SNP', but different people use them all differently. The problem is that a 'haplogroup' is not just one thing, it's a trail of things, that together define a specific branch on the human tree. As an example - if we think of haplogroups as locations, and we asked 4 different people for where they are from, we might get "I'm American", "I'm a Chicagoan", "I'm from Illinois", and "I'm from Oak Park". They're all different! And yet, are they? They may actually all be exactly the same, just different in specificity.
And that's the problem with a stated yDNA haplogroup. Four different brothers might be full siblings but give four different answers, depending on where they tested, and how far they tested. If you were to test further, you too would change your haplogroup.
I prefer the term 'haplogroup trail', the list of SNP's that lead down to a person's current end branch. With further testing and ongoing research, the end of the trail is going to keep changing for quite awhile, but most of the trail will remain the same, especially the notable SNP's (which I highlight below).
My FTDNA 'haplogroup trail' is
My Living DNA 'haplogroup trail' is (based on YFull)
So I could name any one of those, from either tester, as my haplogroup. I could say I'm R-M269 and match the majority of other testers. I could say I'm a R-U106, and still match millions of people, but at least it's a subset. I could say I'm R-S23346, but who would know what that is! I could say I'm both R-Z18 and R-Z19, exactly equivalent SNP's because they are at the same level, but FTDNA named the level Z18, and YFull named the level Z19. By now, you can see the confusion! Not only would you have different haplogroups if you have tested to different levels, but you could have different haplogroups if you tested to the *same* level, but with different testers!
That's why I prefer using 'haplogroup trails', because you can see potential matches, even with different testing levels. If we changed those example locations I mentioned earlier into 'trails',
- America->Illinois->Chicago metropolis
- America->Illinois->Chicago metropolis->Oak Park
Now it's easier to see the potential matching, and the need for more specific info in the shorter trails, more 'testing'. And you can see where they match at higher levels, but differ at a lower level.
Your I-M223 is much more specific than my R-M269, but is still very broad. With more testing, it could change quite a bit, to a branch far downstream from M223.