So the short answer is they seemed to do it somewhat often, in my opinion, so I think your point is valid.
Did any of that make sense? My brain is in a jumble to night.
Makes perfect sense Kass and thanks for your input :-)
Good stuff there Sarushka. Thanks for sharing!
Signing their names through the years consistently in order (as shown here) makes it almost seem impossible that the acronym OTMA wouldn't have popped in their heads at some point and mentioned among each other, don't you think? Perhaps they found it to silly and/or impolite to use the abbreviation on formal letters or more heartfelt notes to family members and friends.
In some ways it seems unusual that it would ever have been used which probably makes sense as to why don't see with anything close to regularity. If each of the daughters intended to sign a note/letter in their own handwriting it stands to reason that they would spell out their full names. Why would Olga, for example, write a letter, sign 'O' and then ask her three sisters to come over to do something as simple and relatively impersonal as penning the remaining 'T', 'M' and 'A'.
Correspondingly the letters I've seen from the GDs written individually don't read like announcements from the group. They seem more personalized making it silly to think they'd sign it with OTMA or anything else other than just their individual names. Olga writing her friend in captivity, for example, is giving an overall picture of their day-to-day lives but much of the content is still personal. It doesn't make a lot of sense for her to sign it 'OTMA' instead of 'Olga' then since the letter wasn't written collectively. Seems to me that all of the daughters wrote quite a bit as well. So if Nicholas stationed at the Front during WWI is consistently receiving letters from all for daughters, to use an example yet again, there wouldn't seem to be much of a need to sign off on something like it's the thoughts and well wishes of all four together, i.e., 'OTMA'.