I don't think that the wish for more left wing party is to make anyone feel better but is a wish to present a different viewpoint, and not let the right wing set the agenda. When Labour moves to the right the Conservatives move even further to the right, and right wing views are regarded as what is normal.
When politicians like Rachel Reeves said in the New Labour years that Labour was not the party for unemployed people, those sort of views gave permission for the Coalition to introduce the punitive welfare reforms. That bill should have been vigorously opposed, not just abstained on. People who are either unable to work or cannot find work need someone to represent them, not treat them as not worth fighting for or people to be put on show for entertainment on poverty porn reality t.v.
The bill to prevent undercover police from prosecution should also have been opposed, not abstained on. Decent undercover police need to be exonerated of crime after a full investigation, otherwise will they not live under suspicion that any crime was just ignored. Also, the women that were lied to and used need to have their feelings known.
More, when the Conservatives and the Liberal Democrats tried to blame the International banking crisis on Labour frittering away money on schools and hospitals, did Labour argue against that narrative, hardly at all, they just said they approved of austerity likec George Osborne. Austerity was wrong and damaging and unnecessary and Labour should have been stronger and argued against it.
So called centrists might well be right that the country prefers a right wing narrative, but surely there should be a party who is willing to try to present a different way.