I don't know if it depletes the body of any beneficial minerals to be honest. It does remove the other harmful halogens I know for sure.

It does increase the need of other beneficial minerals, simply because the other minerals are required in higher doses for the detox process, and to work in concert with Iodine.

Selenium being the highest priority. I take about 300mcgs daily.

Magnesium is another, although I have a pending question about dosage here on another thread.

I have been wondering about myself.

I have been noticing lately that I am getting tighter muscles after taking my iodine.....need more magnesium.
Flechas talks about Iodine helping Magnesium transport somewhere.....

my problem is my bowel tolerance is so bloody low

but if this a sign that things are shifting for me here, that is something to be happy about

Vitamin A for one is needed for the Iodine uptake by the thyroid.
So if you are low in vitamin A the Iodine might not be effectively absorbed.
The same goes for selenium. Excess Iodine can be toxic for your thyroid if you are low in selenium and vice versa.

I am still recovering from 1 mg iodine intake for 4 days. It gave me crazy tachycardia. I thought I was dying. It's been a year since and I am still not 100% recovered. My guess is that taking iodine disrupted my electrolyte ratios. I've been taking magnesium and other things.
So, yeah, I believe iodine sure does increase your body's need in other nutrients.
I also think that advising people to take crazy doses like 50 mg without medical supervision is irresponsible. And to think that taking mega doses of one nutrient disregarding what it might do to the balance of other nutrients is downright dangerous. Iodine doesn't work in a vacuum. Your body is a complex mechanism designed to work best with specific ratios of nutrients.