@Lyndsay
There are always ways to cut costs. For anyone contemplating doing this, compliance with building codes is essential. You saved by cutting corners on building code, and your inspector cut you slack on engineering. Not many places where you can get away with that.
Anyone contemplating this type of build should consider compliance. You can’t make the dig, insulation, foundation materials free. Slabs need an engineer stamp, casting an insitu slab in the air requires an engineer on site to approve forms, rebar placement, cement specs and the pour itself.
The reason for a steel beam is just time and cost. You don’t have to wait a month after pouring the basement floor to support form work on the garage slab, you don’t need to frame disposable support walls. The beam also simplifies and reduces costs of under slab insulation and ceilings.