Obviously you can do whatever you want. You don't *need* an RO/DI filter. Plenty of folks run their systems without them and have success. But everyone's water is different. And even folks with "perfect" tap water are not assured that it will be "perfect" the next day.
But don't fool yourself that household purifiers or filters are the same, or even close to, truly pure RO/DI water. Are they better than nothing? Sure. But they're not pure water by any means. The TDS (total dissolved solids - a parameter used to gauge water purity) of my tap water is 80-90 ppm. If I run it through a PUR filter, it comes out around 40 ppm. So yeah... it cuts the TDS in half, but it's still not pure by any means.
Plumbing an RO/DI unit is far from rocket science. Between the instructions with the unit, and help here, I bet you guys could do it.