Is Free Domain Bad?
Is hosting your website on a free (sub)domain a bad thing?
Of course, you always have to keep in mind that a "borrowed" subdomain, albeit registered in a seemingly standard procedure, isn't really yours. You don't own the domain, so unexpected things can happen to it, e.g. the provider decides to block your subdomain, the provider doesn't renew the domain, Google decides to de-index the whole domain on grounds of spam...
On the other hand, when you're just starting on a website, and you don't yet know how successful it will become, you may want to consider the option that requires no up-front investment.
Let's consider the following two examples.
First example is ours. This website was, in lesser shape and size, hosted on a free CO.CC subdomain for three years! The site had its downtimes, but they were attributed to our hosting provider (which we've switched from since).
The other example is one of our competitor's. They had run a free hosting whitelabel busines on a CO.CC subdomain, and they had provided their free clients with free sub-sub-domans. One of their free clients apparently turned bad and (ab)used the host for some malware and phishing. As luck would have it, soon enough their whole subdomain was marked as harmful by Google, and since CO.CC so readily responds to abuse complaints, their subdomain was taken away from them in such a way that they couldn't ever re-register it. Months of work and clientele building went down the drain. Their free hosting website inaccessible from that moment on. Such shame.
That wouldn't have happended had they used a top-level domain. Their domain would still get marked as harmful, but they would have had the option to issue a "reconsideration request" and eventually get back on track; their website, albeit through Google's warning page, accessible all the time.
Obviously, you get some advantages if you buy a domain, and dire consequences in some cases if you don't. But these are the only real differences between domain and subdomain.
If unsure, we recommend a free domain or subdomain to start your project. But if it ever picks up any steam, as soon as it does, go spend that $10 and confidently redirect visitors to a new home.