But for that one term they're still liable to follow the party whip. They may be less inclined to do so, but this doesn't change the fact that there will be far fewer independents and people from outside politics in the House if it is to be elected.
Replace "peerage" with "senate appointment."
Even if only 20 or so senators are directly appointed, this does not take into account the fact that parties choose their candidates. Granted, STV is an effective way of combating this, but I can't help but feel that most voters will vote as the party tells them (de jure STV, de facto PLPR) and that therefore, promising a candidate the "right" place on an unofficial party list (like a leaflet which tells supporters how they should vote) will serve the same function as promising one a peerage.
If you have 20% of senators appointed for life by an independent commission then that would be a far greater proportion of independents in the upper house than we have at the moment. Furthermore, as we have seen in the past, things like university constituencies are very likely to elect independents themselves.
Of course, why you place such a value on not being formally aligned to any political party is beyond me. I would much rather vote for someone and know what they stand for than to vote for someone who masks their partiality behind the label of "independent".