Fully elected upper chamber

Parliament has now voted to make the House of Lords a fully elected part of the legislature.

From a contemporary democratic point of view, this is a good thing. No more right to sit based on accidents of birth or by virtue of large donations to political parties.

On the other hand, the upper house has recently shown its worth by rejecting bills from the Commons.

Does making the Chamber fully elected make it more likely to support the government of the day?

Is it really a good idea as it sounds?