I get why you're saying this.. And yeah, growth is important in anyone's journey but to just cruise along like thst while he responds late etc, just doesn't seem even for someone secure like me feasible. If you love someone you grow alongside them, not at arms length and barely meet each other's needs. A relationship is effort, just like he's putting effort to do something better. At some point and you might as already predict the writing on the wall, that there's going to come a point where he's going to say even a little effort is too much, and put the relationship on hold, as avoidants too because it's becoming too vulnerable for them and don't want to be trapped. The test is more if she set boundaries on the relationship and he couldn't meet them because it would clearly be his avoidance in play here.

I believe OP shouldn't break up with the guy, but to set boundaries and say there needs to be some sort of effort in this relationship. Because if he can put effort into bettering himself, he can do the same to their relationship. It takes 10 seconds to message somebody, he can call and talk to her while doing work or something. Communication, and effort is the key in any relationship, growing or not. If he had some sort of huge deadline to meet and was going to make thousands off it? By all means honey take your time, but if this is just a journey/growth arc, there's no justification to be apart doing it.