The reason why doctor's don't recommend heme iron is because high intake of heme iron is linked to increased risk of colorectal cancer, stroke, heart disease, and type 2 diabetes, unlike non-heme (plant) iron, which does not show the same risks.
Although some doctors do recommend heme iron, so not all doctor's avoid recommending heme iron, but heme iron is not recommended by all doctors as much as it used to be.
Heme iron acts as a pro-oxidant, that damages cells and DNA, so balance with plant based iron often preferred for general health to avoid iron overload.
A high intake of heme iron is associated with a greater risk of colorectal cancer, lung cancers and pancreatic cancers, which is potentially from it forming carcinogenic compounds in your gut.
Heme iron also promotes oxidative stress and inflammation, which contributes to hardening of the arteries, also known as atherosclerosis, and increases your risk for heart attacks and strokes.
Heme iron is also linked to insulin resistance, type 2 diabetes and metabolic syndrome.
And heme iron can also generate free radicals, damaging lipid, DNA and protein.
Heme iron is animal based and is found in red meat, poultry and fish and is well absorbed, but it also carries health risks at high levels.
Non Heme Iron is plant based and is found in leafy greens, beans and nuts and is less absorbed but does not seem to carry the same risks of chronic diseases as heme iron which is animal based.