Larger life insurance policy to include stepson?

I recently got married and have a 7-year old stepson and I am currently looking into life insurance. I plan to make my wife the primary beneficiary and make my stepson the secondary beneficiary.

My wife has primary custody and my stepson is with us about 80% of the time. Her ex is not great with money: he is in credit card debt and sometimes can’t pay support because of expensive like relatively inexpensive car repairs and then gets behind a few payments and doesn’t make them up.

I looked at a couple life insurance calculators that suggest I would want to get an additional $200,000 – $300,000 of coverage (if not more) if I include my stepson in the calculation as opposed to calculations that only include my wife. I doubt adding that additional coverage will significantly increase how much my monthly premium payments will be.

Some example of how we handle our finances:

We split smaller costs like tickets to a museum or meals 50/50, but she pays for larger costs like a plane ticket for him herself. I invest a little each month in a UTMA some for my stepson and hope to have $5,000 – $10,000 for him when he is able to able to access it. However, there is no expectation that I would save for, or help pay for, college for example.

With all that (possibly unnecessary) background, what are people’s thoughts on getting additional life insurance coverage for my stepson?

Thanks in advance!