However, such a system can't be grafted onto the US without doing terrific damage to separation of powers. The executive (meaning the head of government, rather than the head of state) in the Westminster parliamentary system is a subset of the legislative branch, and it remains, in certain limited ways, subservient to it.
Kind of, but it's not
quite that simple, unfortunately.
In the UK, Parliament is the Legislative branch and the 'cabinet' (in effect) the Executive. The PM, while appointed by and responsible to the Crown is, accountable to Parliament
politically. The office of the PM is certainly not accountable to the electorate - not legally or constitutionally anyway.
The PM is also the
De Facto (not the
De Jure) head of state. This is an evolved role of course, back in the days of (weasel) Walpole and his immediate successors the role of PM wasn't defined as it is now and the role was played in an arguably far more Presidential manner.
The constitution
explicitly ensures the supremacy of Parliament. Yet, the PM and the Cabinet are also members of Parliament, the PM controls Parliament's timetable and agenda. Given the wide ranging powers the PM has over Parliament resulting from Royal Prerogative and other constitutional powers, his ministers (and thus indirectly the Civil Service), power of Patronage and so on any true accountability is weak in
constitutional terms.
However, effectively, there are considerable checks on the power of the Executive. The PM needs the support of Parliament (and to a lesser degree, his cabinet) to Govern, thus a strange situation exists; Parliament
can pass a vote of no confidence (happened last in 1979), effectively sacking the PM. Conversly the PM can (subject to consent of the Monarch) dissolve Parliament and call a General election.
Finally, in addition,
generally at least, overwhelming public opposition will cause a PM to back down, a notable recent exception being Iraq. The decision by Blair to ignore the electorate, many of his own ministers, aides etc even though he was under no
obligation to listen, cost him his reputation. His tendency of behaving in a manner widely perceived as
'Presidential' didn't help him at all either.
This 'stand off' has generally served the UK well, at least in recent history.
The role of the Lords, or rather, what's left of it is largely one of scrutiny and revision. I can reject bills passed by the Commons but cannot defeat them if the Government is hell bent on it, Parliament will invoke the Parliament Act. That rarely happens, the last time (I think) was the fox hunting ban. The main role of the Lords is as the highest Court of Appeal.
That is, of course, not so in the presidential system. The President's powers in no way derive from Congress, and Congress can't circumscribe them.
True, such a clearly defined separation has advantages and disadvantages, as does any system of course. Of course the functioning of a Parliamentary system isn't so different for most every day practical purposes. The end result is usually the same, fudged policies, nepotism, bungled opportunites, partisan backbiting, interest groups and lobbyists getting in the way.
Britain tried being a republic, more by accident than design a few centuries back for a very short while - but decided against it pretty sharpish.
And that's not a bad thing. Looking back over more than two centuries of American history, I think it's safe to say that the country has had more genuinely bad Congresses than genuinely bad Presidents.
I suspect that's very true, the power of the president being subject to checks and balances (and vice versa) can work for good or ill, I suppose.
So far as a recall process is concerned, I suppose one could argue that knowing one may be subject to being shown the door for, presumably being a putz, may focus one's mind. The downside of course being that those deciding said putzness would likely be doing so based on dubious, partisan grounds. This would surely be a serious disencentive for doing things that, though unpopular may be for the best. Separation issues aside, any such process at this level would be open to such abuse it would surely be unworkable.
Besides, a mechanism for removal of the President already exists.