I fully support this decision of yours. I'd consider doing this for all my future games. I joined a group already in progress in a campaign as level 8. The rest of the group except 1 other has magic items from earlier in the campaign before we joined. The other player recently proclaimed she
deserves
magic items since the rest of the party already has them. I'm sure many other people have heard of this happening in other games, but it was a first for me. I almost guffawed -- and no one uses that word lightly. No <<thank you for letting me start at level 8>>. She simply skipped straight to <<Give me priceless objects that require effort for free>>.
I have mixed feelings on this. The whole attitude of I deserve would send warning bells off in my head. I really don't like players with huge entitlement issues.
On the other hand I have joined into games already in progress and the lack of magical items can effect my PC negatively. Especially if I am playing a mundane character who depends on magical items to boots my abilities. So I allow a few magic items based on level.