Pretty much all criminal cases that go through an actual trial are based on circumstantial evidence. I.e. if you have, say, CCTV footage of someone murdering someone, then a guilty plea is likely entered early. Those that claim the evidence against Letby is too weak to convict would probably not convict anyone of any crime where the sort of slam-dunk evidence I've mentioned didn't exist.
On the point about the defence not calling their own experts, this isn't odd at all really. The defence legal team's first job is to prevent their client from convicting themselves. That means avoiding any "own goals" in front of the jury. While the defence could likely have found experts (such as Dr. Lee and his team) that could look at the evidence and say "these deaths can be explained by natural causes" the defence will then test them under light cross-examination. Because the prosecution will be going at anyone put up by the defence and asking Qs in front of the jury such as "can you rule out foul play", "would it possibly be explainable by the explanation given by Dr's X, Y and Z" and "are you saying your fellow medical professionals have got it wrong?" And if they then start waffling or answer in the wrong way that's a disaster for the defence. It's likely that the defence couldn't find an expert witness that could maintain a categorical rule-out stance under cross examination and therefore felt it safer for Letby to go with nobody and let the prosecution try to prove guilt.
Killers and other criminals are often careless with evidence. You kind of seem to imply that the police finding evidence potentially pointing to guilt when searching her house actually implies that she is innocent, which just kind of sums up the craziness around the "free Letby" movement