1 - right now you need HQ materials to create HQ+3 item (assuming rank 50 DoH & rank 50ish synth), correct?
2 - with your proposal a rank 50 DoH would be able to generate a HQ+3 rank 50ish synth by grinding out NQ mats into NQ end goods and then combining the NQ end goods into HQ end goods, correct?
3 - NQ materials are largely worthless (caveat: materials you need to farm for, NM drops, etc).
Therefore your proposal reduces the need to obtain HQ materials in order to obtain top-end gear.
In some cases that point you are making holds (NM drops for example). Even a NQ NM drop is worth quite a bit right now and a HQ is worth quite a bit more (the last I looked anyway). In this case then you could reasonably make a trade off between buying HQ components or NQ components.
For many other cases though your proposal undermines the value of HQ goods even more than they are undermined in the current system. At least in the current system people trying to obtain HQ gear (meaning +3) are seeking out HQ materials.
Aside from that - I could get hundreds of NQ oak logs or anything NQ DoL-able for free (or for whatever the NPC would pay if you want to be more even or even a bit more - so like 200g / item?). So can any crafter with any sort of social circle. That completely undermines your argument because the NQ can be had for 0g (or ~200g) rather than 2k. The trade off becomes "sit around for hours synthing NQ junk that cost me next to nothing or pay a bunch of gil to save some time".
EDIT: I didn't say it because I figured everyone here is smart enough to fill in the blanks but the trade off of spending a lot of time grinding out items that are basically free vs. spending a bunch of gil to save some time totally favors people who will bot crafting and thus runs against some important premises at the heart of how this game has been designed and balanced.