Why is my child's college scholarship taxable if the tuition paid(tuition only, not room and board) is higher than the scholarship?

Your income is not affecting the program other than the Q entry. If you entered the 1099-Q when it should not be entered, the program goes into a tizzy. The 1099-Q is completely used up on tuition and room and board. There is no need to enter it. 

IRS Pub 970 states: Generally, distributions are tax free if they aren't more than the beneficiary's AQEE for the year. Don't report tax-free distributions (including qualifying rollovers) on your tax return.

Just thinking -the IRS encourages you to juggle numbers to your benefit in Pub 970.

1099-Q used on room and board of say $10,000 for an example plus $9,000 of tuition.

1098T tuition of $14,000 - $9,000 used by 1099-Q leaves $5,000 to be allocated.

You could claim $4,000 for AOTC, this would make $2,000 of the scholarship taxable. You would have a big credit and student may not even have a tax liability.

The credit and income limits:

• For the full credit, your MAGI (modified adjusted gross income) is less than $80,000 ($160,000 if you're filing jointly)
• For a reduced credit, your MAGI is between $80,000 and $90,000 ($160,000 and $180,000 if you're filing jointly)
• There is no credit given if your MAGI is above $90,000 ($180,000 if you’re filing jointly)

Things to remember are:

• Most people are always trying to reduce their income so they subtract box 1 from box 5 and enter the difference. People get a certain mindset, reduce income so making the jump to increase credits is hard for them.
• See page 52 for qualified distributions at IRS Publication 970, Tax Benefits for Education.
• Please see my 529 example with IRS information here.
• Tax Benefits for Education: Information Center| IRS

There are three things you can do with your Qualified educational expenses (QEE):

1. Allocate then to scholarships (so that the scholarship remains tax free)
2. Use them to claim an education credit
3. Allocate them to the 529 distribution (1099-Q) so that it will not all be taxable

TurboTax allocates QEE, in that order, until you tell it otherwise. TurboTax allocates QEE, in that order, but it doesn't always  do a very good job.  It's best if you have some idea of the outcome expected, when you make your entries. 

One possibility is that TurboTax allocated part of your dependent's college expenses to claim the Tuition credit, even if you are not eligible or otherwise did not claim it.  It may have also allocated too much ($10K) to the tuition credit.  Look at the student information worksheet for this allocation, particularly line 17 of Part VI. 

Q. Does income play a role? 

A. Yes, indirectly.  If your income is too high to claim a tuition credit, that leaves more QEE for the other two tax  breaks. 

If TT allocated $4000 of tuition to the tax credit, that could account for $1000 of the scholarship being taxable.  Making some of the scholarship taxable is usually the best option, when there is a shortfall of QEE.

Side issue: having a  "$3000 balance owed going into 2023" may be a bad plan.  For a 529 distribution to be "qualified" the funds must be distributed in the calendar/tax year that QEE were incurred and paid.  One exception, you may count payments, made in 2022 for expenses in the first term of 2023.