You can’t get both Carers Allowance and ESA because they are both benefits paid as ‘earnings replacements’. Otherwise known as overlapping benefits.
I agree it’s a bloody complex and stupid set of arbitrary rules. The trouble is that originally the idea of paying people because they were too unwell, or old or had lost their jobs was straightforward. But that was in the 1940s. Since then bits and pieces got bolted on, benefits replaced other benefits, it has all become unwieldy, impossible to understand for the average non specialist (and lots of them too) and should be shelved and replaced with something that works. But that’s virtually impossible to do now because of the vast amount of Acts of Parliament, agencies, departments, rules, jobs, etc,etc which would all have to be scrapped and replaced. At a cost of billions. And then you’ve got to replace all these little bits and pieces, which would again be complex, probably unwieldy, perhaps just as stupid and difficult to understand. And wouldn’t save a penny of Tax / National Insurance money. And we’d be no better off.