Couldn't the doctor have gone fetched Captain Jack to go in that radiation filled tank instead....

Found him easily enough later on.

I think the point was that there wasn't enough time to leave Wilf, grab the Tardis, grab Barrowman and come back again.

That would have been too easy.

OP: Why is your 'Allons-Y' thread broken?

Isn't that the benefit of having a time machine?

Can't go back on your own timeline or something

As long as you're not in the same place twice you should be ok surely?

Could leave the room, go to the tardis, fetch captain jack and as long as he reappears at a time after he left the room he should be ok.... i think.

This was the plot device that you choose to criticise.

No, he couldn't.

Per the Doctor's most recent throwaway comments on the topic, you can't exist twice within the same causal nexus. So you can't be simultaneously doing two things within the same connected set of events. Thing 1 would be running from the room down the Tardis, unhiding it and setting off while the simultaneous thing 2 would be arriving somewhere else and returning to the room. The Doctor wouldn't encounter himself but would be acting twice within the same set of events. You know, assuming 'causal' and 'nexus' have their usual dictionary meanings.

The best way to think of it is: what rules have the writers had to set down so that time can still be a factor in stories.