Now vs. Later and the return all matter...
You trade Byrd now and bring up BJax, you will start his service contract and lose control over an entire year for the team. And in this year, it may be prudent for the Cubs to wait to bring him up. He did not face one full count during the preseason and had a .091 BA/OBP with 2 strikes, so he does have something to work on. No need to rush players just because there is a youth movement.
The quality of player matters too. Theo explained that he would like to turn short-term assets into long-term... Byrd brings little in a trade right now. Worse thing that could happen? He hits like last year and someone takes him at midseason for what they would take him now. Best case scenario, he plays well (better) and someone gets injured on another team, and there is a need for him therefore giving leverage to the Cubs for a better trade.
Build stock, increase trade value, allow BJax to continue improving, stall his service clock...