It's not premature at all to publish the principles of an exit strategy, which is what understand Starmer wants. I don't think he's demanding an exact time line.
A number of issues have caused me concern.
Firstly, there is pressure for schools to re-open as soon as possible. I can understand the problems with childcare for younger children, the fact that there is likely to be an increase in educational inequality and the fact that some parents just do not know with their children, especially if they're trying to work from home.
Nevertheless, anybody who thinks that children can be kept two metres apart in a classroom have either never been a classroom or don't know any children (or both). Teachers have not been promised any PPE and are, rightly, worried about working in such an infection-ridden atmosphere. Children themselves might be asymptomatic but they can be carriers are likely to spread infection through communities.
Secondly, there is pressure from businesses to return to something like normality. Again, I can understand the concerns. People aren't being paid, but rents and bills continue to mount up. A recession is certain.
However, more businesses open mean that more people will need public transport, leading to overcrowding and putting transport workers at risk. People interacting in the workplace will lead to increases in transmission.
The kind of exit strategy we should have would be termed in general principles, such as "we will do X, only if Y happens" or "we won't do X, if Y is still occurring" or " we will put … strategy in place to protect key workers" or "we understand there is a trade off between the needs of business and an increase in infection rates, so will do …", etc etc etc.