I would like to add a few observations to cloudsourcetax’s excellent comments and, in particular, on the first bullet point.
If the arising basis is used, the more accurate way of looking at the tax situation on US dividends, interest and capital gains is perhaps to say that UK tax will be payable, and the US should give credit for the UK tax against the domestic US liability. The question is then whether there is a material overall increase in the total tax burden.
The other factors to consider are the use of the remittance basis deprives the income tax personal allowance, the capital gains tax exemption and, on dividends, the dividend rates of tax on any dividends that are remitted. Plus, if the arising basis is used, there is no build-up of contingent tax on unremitted income and gains and the work in tracking non-remitted amounts.
On US dividends, my calculations show that there is not generally a material additional overall tax if the arising basis is used.