I think it might be due to ingrained social etiquette, maybe? Almost like the really old "knight in shining armor" thing where the guy is always the one pursuing the woman.
And I know exactly they how they feel because I'm doing exactly as you describe as we speak LOL I'm not even entirely sure why. I went out with a guy once, was just like you described they are and made it clear I liked him, but I have never messaged him first. It's not a lack of interest or any of the other things you said, in my case, and I suspect many others. A part of me says, "If he really wants me, then he should show it!" Then I'm like, "Doesn't the same apply to me?" But then I'm like, "Nahh, he's gotta do it or it ain't happening." I don't know why, sorry!
And go ahead and pretend I'm a girl for the purpose of your question and my answer, cause I'm definitely acting like one.
It's even possible the girl is thinking constantly, "Why isn't he texting me!" and complaining to her friends but still won't text first. I've had girls complain to me like this. If I ask, "why don't you just text him?" they'll moan, "I caaaaan't." Sometimes they worry they'll come off as needy or something.
I kind of go back and forth when talking to girls if I start to feel I am always initiating a conversation, one of two things usually happen:
1. I decided they are not that interested in me or just using me as a sense of entertainment and/or validation, to test this I usually do:
2. Purposely stop texting to see if they start a conversation if I wait long enough, if they do not initiate a conversation again I figure that my first conclusion is right and they will move on to talking to someone else if they haven't already.
However if they do message me I take this a good sign and continue as normal, eventually I ask them out if I feel things are going well enough and they seem to be responding at regular intervals and in a consistent way.
But if I start to see signs that their interest in waning (i.e. they start responding with more short answers, start taking longer to respond, seem less enthused or interested in talking, not contributing to the conversation, etc..) that is when I do the same or just cut them off all together as they are not worth my time and energy.
I have learned if you text to much or are always the one to start a conversation it usually comes off as clingy or desperate and/or it becomes the expected behavior and I feel it should go both ways and it should be equal levels of effort from both people if they are both interested in each other, I have read lots and lots of forum's and articles and the general consensus seems to be this, if a girl likes you she will put forth the effort to talk to you or be around or spend time with you, if you ask a girl out and she always has an excuse or says she is busy, move on as she isn't that into you, if she hasn't responded in more then a few days to a week to a message or phone call, do not message more then once or twice after 24 hours, give her a few days (I would say 2-3 at the most) to respond just in case, stuff does happen, but if you do not hear from them assume she is not interested anymore and has ghosted you (or possibly something has happend and she can no longer use a phone or communicate, what ever that may be), accept it and move on to the next one.
As a disclaimer, I have had a very poor luck with dating myself, I can get dates but they don't usually go anywhere, I have only be in a hand full of relationships in my 31 years of life, the things I have said here are my own experiences and opinions and should be taken with a grain of salt as everyone's experience varies.
I am sure I am not the greatest catch out there, I am overweight, balding, pale, hairy, lazy, introverted, blunt, don't make a lot of money, don't have a very nice car, don't have the best sense of style or humor, I am opinionated, stubborn, have self esteem issues (obviously), and not very confident when it comes to relationships and females. However I am intelligent, I am resourceful, I can be sweet, I can be thoughtful, even sometimes romantic, I can be charming in spurts, I can make people laugh, I have on many occasions greatly impressed people, I am talented in many things, I am good at what I do for a living, I am fortunate to be where I am today in my life and career, and I have ambition.
I have my pros and cons (probably more cons then pros, depending on what someone values in a partner), but the point I am trying to make is try to just find someone who likes you for you, someone who makes an effort to talk to you and spend time with you on their own and/or at least putting forth as much effort as your are putting in, and I am not a shinning example of this but try to just be yourself, don't try to be someone who you think someone wants you to be.
Best of luck,
Brent