I would support this but we need to be somewhat clear about why and when we want to push people to those sites. I actually prefer this to adding those sites to our list of migration targets because we can tell them very explicitly how they can fix their question here (pointing at our site) as well as what is expected over there (hand wave), instead of just pushing them away.
Out of preference we want to keep people asking quality questions on our site so our first priority is getting them to reword their questions to be on topic here. Failing that then we want to push them to the other site.
My preference would be to keep the "product, service, etc" close reason for when the question is vaguely asking for some unknown something that might do their job.
Questions seeking product, service, or learning material recommendations are off-topic because they become outdated quickly and attract opinion-based answers. Instead, describe your situation and the specific problem you're trying to solve. Share your research. Here are a few suggestions on how to properly ask this type of question.
And then change the hardware shopping close reason to be both hardware/software recommendation:
Questions seeking hardware and software shopping recommendations are off-topic here. Instead of asking what to buy, try asking how to find out what suits your needs so that we can help you solve your problem. If you are simply wanting a hardware/software recommendation then you may wish to look at our sister sites [hardwarerecs.se] and [softwarerecs.se] but first consider whether your question meets their quality guidelines. You can find their guidelines at [Link to HWRecs guide] [Link to SWRecs guide].
The problem here is that it makes the close reason very long and a wall of text which many people are not likely to properly read beyond "blah blah not welcome here blah blah".
Shortening the total wordage would be good, but keeping the overall meaning and intent of keeping users here is more optimum.