There should be no reason why you cannot use the proceeds towards paying off other debt. A home equity loan is typically a second mortgage which constitutes as a cash out refinance. If you qualify for the new loan, the lender has no business telling you how you can and can't spend your money.

On a side note, you reference using your home equity line "towards the house." This infers your participation in a home loan accelerator program. Although some may beneift from such programs, with inflation looming around the corner, having a fully adjustable rate could lead to a significant rate increase and substantially larger payments.

To digress, paying off high interest credit cards, is definitely smart use of a home equity loan.