No, not exactly. It's been my belief that the Senate majority party has every right to demand a "moderate" (center-right / left) justice, but it shouldn't go beyond that (eg: unreasonable to demand a completely centrist justice, or justice from the opposite ideology of the president, however you want to measure that).
If in the majority, Democrats would be completely within the realm of reasonableness to vote down someone like Scalia or Thomas, for instance. And I wouldn't blame Republicans for voting down someone like Thurgood Marshall.
The Supreme Court has incredible power to sharply change the the rules and levels of power that govern this country. It seems downright absurd to me to not take into their account their views when deciding whether to confirm.
I don't think that is a stable system, even if the Senators tried to implement it in good faith (and getting the parties to agree what is a centrist mainstream judicial philosophy will be no easy task). And over time, if the Pubs controlled the Senate mostly, when the Pubs also held POTUS, there would be conservative nominees confirmed, and when there was a split, they would be moderates. Over time, the conservatives would tend to be a majority. If POTUS had the say, then the Dems would not have that deficit, and the system is much easier to follow and implement.