See my comments below.
The best solution to this problem is to put your HP Printer on Craigslist for about $10 and you might sell it. Otherwise, throw it in the trash and buy a good printer from another brand.
HP support is the very worst. As you can see above, the solution to every problem is to install their bloatware. Don't do it.
You are also correct in that the printer will always default to normal printing.
I had this issue for years - no matter where or how I set the default to draft (on the very same printer), I will always default to normal.
HP is trash. Their computers are filled with bloatware and garbage. Don't buy HP anything. They are the General Electirc of tech products. As you know, GE is a disaster on appliances...... same idea.
This is absolutely the best advice and solution. It is the truth.