R2-D2's introduction in The Phantom Menace works on its own terms because up to this point in the film all the droids we've encountered have been portrayed as expendable, malicious, and/or stupid. Also of some note is that we don't just immediately and arbitrarily cut to the astro droids. There's a justification in that Obi-Wan has to his exasperation been put on Jar Jar duty and has to stow him somewhere, so then Jar Jar tries to make friends with the other servants. And then Padme gets sent down to the droid hold to clean R2, because she's disguised as a servant, and that's how she meets Jar Jar. This meeting later proves pivotal when she reveals herself to be the Queen, and simultaneously declares herself Boss Nass's "humble servant."