If there's a way to remove the Nature2 I would do so. You do NOT want to leave the cartridge in, but they've shafted you so you have no choice but to use one, unless you redo your plumbing (probably not hard) to by-pass it or remove it.

With a new masonry pool, generally, Tri-Chlor tabs can work very well. Such pools tend to have a rising pH as they cure, and Tri-Chlor is very acidic so it can offset some of that. Also, new water needs a certain level of CYA (Stabilizer) and Tri-Chlor adds 6ppm of the CYA for ever 10ppm of chlorine.

Being in Texas, you may WELL want to run your pool with a CYA of 80. That's generally high, and your recommended FC level is between 5 and 10 ppm, but it may well keep you from constantly losing chlorine and risking an algae bloom.

The numbers your builder said of an FC of 1 with a CYA of 30-50, even with a Nature2, is a sure-fire way to get an algae bloom--in a hot place like Texas.

I'm also surprised at the builder's rec of 200-250 for CH. Normally, 200-400 is the recommended range for a masonry pool, with a TA range of 80-120. (However, with a new pool curing and their tendency to increase in pH, a lower TA would be called for to buffer that--that's why his rec pH is to the low side.)

Phosphates don't cause algae--they feed it. If you don't have algae, NO amount of phosphates will cause it. In fact, in all the years I've been here there have been maybe 5 cases where phosphate remover was appropriate.