The key thing is that the business pays corporation tax, it isn't a personal tax. You then draw your salary or dividend payment from what is left.
So when you calculate PAYE v dividend, corporation tax shouldn't even factor into the calculation.
This is hilariously clueless. If you own the company, then corporate tax removes some of your profits. Which is perfectly reasonable. But it means that the funds available for dividends are lower. So, if your company bills 100k, and you have to pay out £20k in tax, you only have £80k remaining to pay dividends on.
The thing that a lot of people forget is that the slightly more tax efficiency of a small LTD was designed to encourage the creation of SMEs and to help them survive. In particular, cash flow is a HUGE issue. So by having relatively low salaries with dividends paid out periodically, these businesses can better manage their cash flow and put aside money (theoretically) as it comes in for both corporate and personal tax payments. Last week, I was chasing multiple large (for me) invoices from clients that had been issued in December and January. The total of invoices that had been issued in the 30-90 day period that had not yet been paid was equivalent to what I draw from the company for two months (salary and dividend). It was reassuring to know that if they hadn't been paid on time, I would only have been forced to pay salary and could delay the dividend payments.
And yes, of course there are other tax efficiencies. eg, my computer was purchased as a work computer. But I benefit on a personal level as well. Obviously as I also use it for non-work related activities (like mumsnet). Ditto my phone. But I'd argue that was true when I worked for a corporate too - they knew I used my computer/phone for personal use. But while there are some LTDs who completely take the piss and put everything through the business, most of us have accountants who don't recommend that. Mine would question anything that was obviously frivolous and would highlight any risks /illegalities.
Finally, another reason the government wanted to encourage SMEs is because we are significant drivers of the economy. We employ people, provide services etc.
The below comes from the government's business briefing in 2019:
"The usual definition of small and medium sized enterprises (SMEs) is any business with fewer than 250 employees. There were 5.9 million SMEs in the UK in 2019, which was over 99% of all businesses.
Micro-businesses have 0-9 employees. There were 5.6 million micro-businesses in the UK in 2019, accounting for 96% of all businesses."
Admittedly, we're not responsible for the bulk of income or employees but it's significant:
"Although the vast majority of businesses in the UK employ fewer than 10 people, this sort of business only accounts for 33% of employment and 22% of turnover."