Looking at the Azure portal you can still get 12 months of free access to SQL Database https://azure.microsoft.com/en-us/pricing/details/sql-database/ unsure what level that comes in at, my guess would be basic, but unable to check as I already have an Azure subscription tied to my account and I've already surpassed the 12 month mark.
Yeah Azure can get expensive, it depends on the amount of DTU's or eDTU's you need, they have a calculator here[/url] where you can upload your metrics and they will suggest what grade database to go for. But its like everything there is a tipping point, some purposes may be cheaper on premise, some in the cloud. You have to factor in all the costs, electricity, cooling, licenses, network bandwidth, servers, storage, maintenance, man power, depreciation etc, everything has a cost and everything will have a break even point. Then again you could say the same for AWS, Google Cloud, IBM, RackSpace, Node4 etc etc you need to find the balance between how much you want to manage vs how much you want the cloud provider to manage.