No need to apologise, a polite "I ran X which solves Y" related to the post is encouraged. Helps the rest of us learn about other solutions out there :-)
I've found that candidates have little or non appetite for take home problems.
If they are busy interviewing, putting aside 2-3 hours (which is not much really) per interview, limits how many they are willing to do per week. As its still a candidate driven market.
Keep in mind, people have to find the spare time while doing their jobs and living life. If they have a family - good luck finding spare time :-)
The best win/win I've found is to pair with someone for about 30 minutes. You help each other, just like you do in real life.