Apple allows free-to-paid demo apps on iPhone
Apple has been pretty strict about rejecting demo versions of apps although "lite" apps have been allowed. Basically, developers weren't allowed to give away a feature-crippled free version of an app for the purpose of upselling customers to a feature-complete paid version. That rule made Apple look harsh compared to competitors like Android, which offers a trial period after which users can get a refund on an app they don't like. If Apple isn't going to do something like that, allowing demo capabilities is the next best thing.