You are right that he is young and has much of room to improve so being patient could work out for him. But you also made good point that if he wants to play for national team regularly he might need to think about joining another club where he has guaranteed more playing time. This is common problem for talented young players do they stay at big club and fight for chance, or do they move to smaller team to play more and develop faster?
Playing at a big club is inherently risky, and it's rare to get regular playing time until the coach truly trusts you. Hendrick might face the same problem as Rodrigo, but we can see Xabi Alonso also utilizing the abilities of young players to develop the team. If he has the option to join another team to maintain his chances of playing for the national team, it might be worth considering, but staying at Real Madrid at such a young age could also be very beneficial for Rodrigo.