There are a few things at work here that make your question hard to answer briefly.
First, the Stack Exchange has a long tradition of wanting to keep "fluff" out of its questions and answers. (It's not a unanimous sentiment by any means, and you can read some of both sides of the debate at this meta question.) Also, the help center for every SE site also boldly proclaims:
Ask questions, get answers, no distractions
This site is all about getting answers. It's not a discussion forum. There's no chit-chat.
So, realize that you are getting into a community that has a good number of members who feel like they are doing a service by editing out comments that some might find unhelpful or distracting.
On the other hand, SE also has a longstanding policy about being nice, and some would argue that a few welcoming comments like the ones you mention in this meta question would be in keeping with that spirit.
Now I'm a little concerned about the way you've worded your question here, which almost makes it sound like there's an epidemic going on within ELL. I've checked all 12 answers you've left on ELL so far, and I could only find one that has been edited by other users in the community. Let's break that down, starting with my edit:
First, you started off by saying, "Great question..." I let that stand. In your last line, you added, "I hope this helps." I let that remain as well. However, I did delete this comment:
Feel free to ask any follow-up questions and I'll do my best to respond.
I didn't think that should stay in the answer, mostly because it's not unusual for newer users to ask follow-on questions in an answer box, which is something that does go against the grain of the SE format. Even if you meant for the user to ask other new questions, I thought your exhortation could be misinterpreted, so I took it out.
Therefore, I take a little exception to the way you've worded this:
I believe as an educator and human being that we should be allowed to include phrases of encouragement and, furthermore, that these promote a positive culture on the site. This is especially true in the case of moderation.
As a moderator, educator, and human being, I agree with you, and I think that my edit did just that. (In fact, the main reason I edited your answer was to improve the format of the arrows, by replacing
Now, there was another user – not a moderator, mind you – who came along later in a separate edit, and removed the "Hope this helps." No doubt this user believed he was doing his civic duty to remove fluff from answers; however, this particular user also has a bit of a reputation for being a little zealous, heavy-handed, and legalistic at times. I disagree with that edit, but it's worth adding that you'll find several long time users of the Stack Exchange that would have no qualms with it. But my point is that these were two separate edits and they should be analyzed as such.
Why are we removing kindness and encouragement?
A lot of your kindnesses and encouragements have been allowed to stand, and I think your question here perhaps mischaracterizes what is really going on. (In fact, I've found seven instances of you starting an answer with, "Great question, O.P.", and none of them have been edited out.)
SE...can also be rather nit-picky in its moderation
Yes, but don't confuse moderation with edits from members of the community who have sufficient reputation for editing privileges. Those are not the same thing.
Why do we feel the need to be so rigid?
There are a few in the community who seem to thrive on such rigidity, but I think the majority of the community doesn't get wrapped around the axle about such minor things. Please don't confuse the actions of a few pedants with the attitudes of the community at large.
One last comment: I'd ask you to keep an open mind about keeping chit-chat to a minimum. While some find that approach to be aloof or even downright hostile, many SE users enjoy the way the sites aren't cluttered by jibber-jabber in the same way so many other online forums tend to become. So, what you might initially find cold and sterile may be the very thing that keeps other active users coming back. That's worth remembering.