They would be more accountable if they were elected as they would have more people to answer to, giving the public more of a say, increasing legitimacy
The House of Lords should be elected due to democracy and they should be representative of the public, removing the elitist nature of the House as members are currently upper class or aristocracy
The Lords may become more competent if they were elected as there would be more people with specific expertise
It would help provide a stronger check on the executive with more scrutiny of the government as a legitimate House, challenging the dominance of the executive
Reforming the House of Lords would go against tradition which would bring a lot of other traditions and conventions into question which may also need reform
The Lords should be unelected so they don't have to worry about being elected so there is no incentive to vote a particular way and they can vote based on their personal opinion, expertise, and knowledge, independent of party politics
Reform of the HOL would take a long time and it would be difficult for everyone to agree to a particular change as there are so many things to consider
Both Houses claiming democratic legitimacy would lead to conflict and/or legislative gridlock
The current appointed House already has expertise and independence and is still functional while not optimal