Typically 32 bit OS can support more than 4GB of RAM (up to 64GB, with PAE) but Microsoft want extra money, although they would be slower.
Main problem is that you have a processor that support x64, and you use windows x32, you're purposefully hammer your computing power by a large gap. All general Intel and AMD CPU as of 5 years ago are all x64 CPUs.
Though, x64 tends to consume more RAM but it is marginal in desktop. The RAM consumption is only noticeable in pico application, such as cellphone, small router/network switches, printers, and otherwise, very small server and application computer. RAM is rather scarce in those devices (small router = 16MB - 64MB, cellphone = 128MB - 1GB, printers = 2MB - 128MB, switches = 1MB - 8MB, small application server = 128MB - 1GB)
Any PC can have a 16GB for under 100$ nowadays, comparing to just 3 years ago, it would cost you well over 1000$ for the same amount of RAM. Having each application consume about a few dozen MB more in 64 bit doesn't make a big difference when you have tons of RAM.