Water Softeners and Air Filtration Systems - do i really need a filtration system?

so i had this house built in October. It is Well water. When we moved in the pressure in all the bathrooms upstairs and down was great but the kitchen sink which is one of those faucets with one handle only had good pressure with hot water only and the cold was very very low pressure. Also in the kitchen i have trouble regulating the temp, it is either scalding hot or cold, no in between.
We have a one year warranty on the house.
I called the builders and their warranty guy comes in to look at the kitchen sink and says the problem is that we need a filtration system becuase sediment is building up.
all of the other sinks work perfect. My beef is that it has been like this from day one.
I had a guy come in to test the water and he said it is not that bad and drinkable.
Here are the results.
the PH was 6.2
the iron (which is measured in mg/l where 1 ppm=1 and anything over .3 ppm usually means staining) was measured at .8. Granted we do get some staining in the toilets only but thats it. Dishes are perfect and clothes.

Manganese was also 0. I am just wondering why the cold water is so low pressure in the kitchen sink only.
The faucet is made by MOEN.

forgot to mention i have all pvc as piping.

It seems to me that the sediment would not cause the problem that fast. If it happans to one faucet, it should happen to others. I believe the guy is BSing you.