This question became almost rhetorical. Today the inexpensive hosting for the small project costs about 5-6 dollars a month. Thus owners of a resource have an opportunity to use all modern technologies, including php, mysql databases and many other things. Nevertheless, thousands of sites continue to use a free hosting, despite its apparent defects and limitations. Perhaps, there are some deep waters in this question? Or we do not take into account all factors? So, yes and no.
A free hosting, as a rule, allows to create only the most simple sites consisting of a set of HTML-pages. Sometimes it is possible to use the built-in forums or guest books, however, very limited on the possibilities. For example, without registration of users, without possibility to moderate a forum or a guest. Any site control systems are out of question.
One more point is that for CMS functioning php and mysql are necessary, but no free hosting provides this. Besides, more often a hosting company that is giving a free hosting, uses sites of clients for advertisements allocation. And, opening a site on a free hosting, you will have to reconcile to presence of banners and pop-up windows on it. In the end of all the domain name will belong to the hosting company. The free hosting can be used for personal pages (e.g., I and my hobby), noncommercial projects, as trial platforms. Serious projects, which aim to get income, or corporate sites in most cases use a paid hosting.
Advantages of a paid hosting
A paid hosting is a possibility to use all modern technologies for a web-resource creation and support. An inexpensive hosting allows to open a site for a small or a moderate-sized firm, or a small project. Large portals use more expensive tariff schedules. But in any case each project receives qualitative services.
Even an inexpensive hosting allows to use php and mysql (from one to several databases). This means, the project owner can install a content management system (CMS) without which customization and service of a today’s web-resource is very hard. Besides, it is possible to make a qualitative forum, the guest book, to add popular scripts (for example, voting, the form of a feedback and other). All this will make the project on an inexpensive hosting much more interesting and more attractive in comparison with the limited free hosting.
An important question is a domain name. Any paid hosting, including an inexpensive hosting, allows to use a domain name of the second level ( .net, .com, .org etc.). Thus the domain name belongs to a client of the hosting company and is his/her property. Besides, to promote a site is possible only if the site is located on a paid hosting. For promoting sites on a free hosting it is required more efforts as search engine crawlers consider them less serious. By competitive queries it is almost unreal for the sites on a free hosting to be on the top of a search engine result page.
Thus, even an inexpensive hosting gives much more advantages, rather than a free hosting. The paid hosting is a metric of solidity of a site and gravity of intentions of its owners. Also in case of a paid hosting there are defined all legal issues connected with the property right for a domain name and a web resource. If you are limited in resources, an inexpensive hosting will allow you to open and to develop successfully your own project in a network. It is good that the question price is insignificant: only 5-6 dollars a month.