Compliance with SID
Your Instructor might be right in a sense, but
there are some airport that you should comply with the initial constrained departure altitude even when cleared to a higher altitude.
If I were the one flying, I will just pre-set the altimeter to FL140, so as to comply with the noise abate proc., then clean-up, approaching 5000' confirm with ATC if you're still to comply with the altitude restriction; when cleared, just pull alt sel and have that "Thrust Clb/ Open Clb" read out.
I think with this, you complied with all the Dept Alt constraint.
Accel at 3000', 5000' initial alt constraint and the cleared alt of FL140.