So what - with all the evasion they engage in, they provide little to the local economy
Corp tax doesn't go to the local economy either.
Neither does the PAYE and NI the employee pay, nor does the Corp NI on those employees. Those go to HMRC. The government makes plenty from indirect taxation of these orgs, and corporate tax is a mere topup.
Only the rates/council tax (and possibly rent for council owned buildings) and the retail outlet of said org contribute locally.
people are will still be here, they still need goods and services; so having UK based companies supply those (and pay their taxes) would be to the betterment of the UK.
Whether a company is international or UK based, the majority of revenue comes from indirect taxation, and the creation of jobs and thus a local economy. Ask Sunderland how much it would like Nissan to go home, which it would consider if you bumped up corporation tax.
Also, read this: