We are starting out a new project where I work and one of the things being talked about is the name of the product. The rest of the company seem to place great importance on the domain name being available eg. [product].com. I am saying that it does not matter as [product].[companydomain] or [companydomain]/[product] are just as good and are obviously available.
Am I talking nonsense? Is there a strong argument for holding a domain with the name you want?
Marketing people do like domains, because it's cooler to print [product].com on a brochure than [something]/[somethingelse]/[product]. Given that domains cost something like $10/year, it's not a big deal.
On the other hand, if your brand is already strong, [strongbrand]/[newproduct] could be better than [unknownproduct].com. You could even combine the two; just get the new domain, and redirect it to your company's site (or vice versa).
Nowadays, we should say that a domain is a "doname"... People is going to learn about your product in the internet, and that means to be as "clean" as possible. So my advice is do have a domain for every product, even if you may unite the name of the product with your general brand...
To get to your gmail account do you go to google.com/mail or just to gmail.com.
Would microsoft.com/xbox be as effective as xbox.com?
I think it does depend massively on your company and the product you're creating. However, there is a lot of impact created by a product.com domain.
As well as the reasons already mentioned, you should definitely make sure the domain name is available, otherwise someone else will end up getting a portion of your traffic. They may want paying to redirect it to you, they may sell you the domain for a fortune, or they may try to sue you for using their name...
Any way you look at it (lost revenue, paid redirection), you will lose some money if someone else owns the domain name for your product.