Almost a fair point but he was adored at Oldham and didn't leave due to not making the grade. He was forced out because they couldn't afford him after playing 44 times and scoring 8 goals. Not sure why people keeping making up their own narratives on the young lad. Just pop on Twitter and you'll still see Oldham fans supporting him. They had a whole Free Jack Byrne campaign when he was benched because they wanted him on the pitch. Your Daryl Horgan comparison makes sense and it's certainly no sure thing that Byrne can step up but there's more evidence supporting the claim than there was with Horgan. Jack has played and thrived in the Eredivisie (some great youtube videos of him against Ajax etc if you're interested), has already played and made an impact for Ireland and has lit up games in the Europa League with Rovers. In 4 games in the EL he had 5 assists and a goal. Different level to Horgan for me.
I also don't see anything that obviously points to him not doing it in training and doubt you have any inside track into who is willing to spend what on Byrne unless you're Graham Barrett? He is out of contract at the end of the season so anyone looking at him won't be paying anything if they wait until then and in the current climate that's what they will do.
The reality is he is fighting for a specific role on the team and there are 2 players ahead of him so he needs to be patient and wait for injuries or a change in approach from Kenny. He isn't competing with Cullen. He will get another chance to build on the start he made against Bulgaria.