It's hardly surprising Keir Starmer is doing well in the current climate. He's a former lawyer and skilled at forensically examining an issue and prepares himself accordingly. When you factor in the stripped down state of the Commons at the moment Boris Johnson hasn't the braying Tory mob to support his bluff and bluster so has shown himself to be woefully ill equipped to engage in debate based on facts. Another advantage is that Starmer, as far as I'm aware, doesn't have the baggage of Corbyn - Marxist, sharing a platform with Hezbollah, support for the political utopia that is Venezuela etc. - so the right wing press are finding it hard to find anything on him apart from the fact he brought his parents a field.
Where the public will judge Starmer is in his success of purging Labour from the radical left (especially Momentum) who seem to have such a powerful grip on party strategy, an acceptance that the British public is inherently socially conservative, and by that I mean they care far more about family, community, law and order, immigration, employment than they do about say, trans rights and gender politics. He needs to be brave enough to debate these issues publicy and show Labour has a strategy rather than ignore those that are uncomfortable (e.g. immigration) then imply that people are racist, transphobic or just plain stupid if they don't adhere to the ideology.
Just as importantly he needs to use his forensic brain to publicly demonstrate his understanding of the reasons why Labour lost the last election so spectacularly and what he's going to do about it. This latter point will inevitably require him to criticise the performance of Jeremy Corbyn and his strategy which, in my opinion, he failed to do with enough conviction to convince people he's not "continuity Corbyn".
Until Starmer shows he has the guts to carry this out then there is no way he'll win back the working class voters in the traditional Labour heartlands who "lent" their votes to the Tories and those turned off by left wing, identity politics. It's not a sufficient argument to say "vote for us we're not the Tories" but I can see the Tories' poor showing during this Coronavirus crisis playing into this attitude. However, we shall soon see as the lockdown starts to ease but Starmer will have to tread a fine line between criticism of the Tories' performance and being accused of political points scoring. I'm not convinced that a Labour government would have done any better had they been in power.
I do agree that this country needs a strong and credible opposition, of whatever persuasion, to hold those in power to account otherwise our democratic process fails to work effectively.