Different answers may be the right "fit" for different families.

Some may want to matriculate as college freshmen, setting aside any potential college credits, essentially counting them for high school only. In this case, holding an Associate's degree would be a downside.

My 2 cents:
If the above does not apply to you, then have your children accept the Associate's degree.

Reasons/perspective:
1) May transfer to 4-year college (aeh posted a helpful transfer list)
2) Requirements can and do change... what qualifies for an Associate's degree, major, minor, etc, at one point in time... may be different a year later.
3) One never knows when there may be an accident, illness, natural disaster, etc, which may interrupt education plans. If any reversal of fortune should occur... according to the US Bureau of Labor Statistics (BLS), it is better to have the Associate's degree credential than to have "Some college, no degree".
Originally Posted by BLS
The U.S. Bureau of Labor Statistics (BLS) designates 1 of the following 8 education levels that workers typically need to enter an occupation:
1- Less than high school
2- High school diploma or equivalent
3- Some college, no degree
4- Postsecondary non-degree award
5- Associate’s degree
6- Bachelor’s degree
7- Master’s degree
8- Doctoral or professional degree
In a graphic at the linked article, the Associate's degree is shown as making one eligible for another 10% of jobs in the job market, as compared with Some college, no degree.