jjosephs:
If I got a monitor with HDMI input why would I even need Arduino or Rasberry Pi in the first place?
Your idea is not feasible; even if the Arduino did somehow have the processing power and the needed pins for the row/column drivers that an LCD/OLED uses (have you ever taken one apart?) - you'd still run into the problem that such a display is not cheap. The electronics that drive the display are the cheap part - the display itself is fairly expensive.