The 1/2" square is about 2.5. as strong as the 3/8" square.Pretty much every company makes them. Specifically 1/2" female to 3/8" male.
Why is it not advisable to use it? Are 3/8" sockets weaker than 1/2" sockets?
What is the proper application to use these things?
Why is it not advisable to use it?
if used properly, adapters are a worthwhile addition to your tool lineup.
Good chatter fellas. Learned a bunch and turns out I just need a brain. Who makes the best brain? Snap-on?
I use them often and have never had a problem.
I use them for adapting the socket I want to use to a 1/2" impact. I don't have a 3/8" impact so the adapter is a must. My sacrificial 3/8" socket set might hate it, but I don't do it that often.
Use them all the time. There are places my 1/2” drive ratchet or breakbar won’t fit while using 1/2” drive sockets. They will fit with using 3/8” with an adapter.

Snap-On makes the most expensive brain. Whether it's the best or not is up for debate. Some people think that the Harbor Freight ones are just as good.
Plus, without them how could you have these extremely useful combinations.
<a href='https://postimg.cc/image/gdr546jin/' target='_blank'><img src='https://s19.postimg.cc/9aj9oke37/Sleeve_2.jpg' border='0' alt='Sleeve_2'/></a>
<a href='https://postimg.cc/image/m8b4y9k67/' target='_blank'><img src='https://s19.postimg.cc/k3qrx6ijn/BS2.jpg' border='0' alt='BS2'/></a>
You just never know when you need the extra torque of a 40" breaker bar on that 1/8" fastener!