Ultra tiny houses are a very poor tradeoff. Your costs per square foot drop significantly as you increase the buildings dimensions. The actual costs are mostly for land which sit unused around them. At that size a 10% larger investment in construction builds a significantly larger structure while still representing a small percentage of the monthly cost.

By comparison of construction vs land. 50k gets you a nice prebuilt 750sf single wide that can be delivered just about anywhere. Which could be covered by ~300$ mortgage meanwhile that much smaller space is renting for 1,600+$/month. So, at best your reducing that 300$ a little while leaving the 1,300+$ land cost alone.