What matters is not the English words, but that you'd making currency-arithmetic more complicated.
I don't think you're making it more complicated. Making it different, sure. I'd argue simpler for everyday mental arithmetic, as you're no longer working with large numbers by default, even to do small value calculations. Many people struggle with a sum like 70+52 or 134-79. Twenty is less daunting to deal with.
Look at the expression £0.15 - that's the same as 15p - so conversion is easy and follows exactly the same rules for decimal points that you would use for ordinary numbers.
But there's no conversion there, you've not actually demonstrated anything, just shown that there are two notations. I know that the 15p is 15% of 100p and is therefore 0.15 of a £, but of itself that's of little use, and less in day to day mental arithmetic. It also lends itself well to a form of maths teaching which I don't think helps anyone - fixating over percentages and moving the magical decimal point around. It's not a particularly helpful way of looking at things for the numerate, and I suspect it does far more harm than good when the innumerate are just baffled by it.
But if you're using £'s and shillings, what does £0.15 mean? Normal rules of arithmetic would say it means 0.15 of a £ which would presumably be 3 shillings. But surely you'd want to write 3 shillings at £0.03, not as £0.15, wouldn't you?
I wouldn't suggest writing a non-decimal figure in decimal notation, no. Why would you want to? Where does that leading padding zero come from?
It will very quickly get very confusing. Or to take another example, how do you convert 75 shillings to £'s? If it was 75p, it would be trivial - just move the decimal point to make £0.75. But if you're working in shillings with 20 shilllings to the £, you have to actually do a calculation to convert.
There's that magical decimal point. You're talking about moving it with an example where it didn't exist, and if it had it wouldn't have needed moving. Your example isn't equivalent in a decimal system - in one the value is less than a pound, in the other it is over. The equivalent would be 75 shillings vs. 375p. In one I need to know there are 20 in a pound, the other 100 in the pound. In day to day mental arithmetic you wouldn't start from 75 shillings, the shillings would have been converted to pounds as they reached 20. The same actually happens in decimal, but we pretend it doesn't because the notation allows easy representation of numbers far too large to be comfortable with.
Of course all of those problems can be solved. You could invent a new convention for representing shillings, and you could get people to learn the calculations. But you're still making things needlessly hard, when working in units of £ and £/100 is so much easier.
All you need is to multiply and divide by twenty, which is no harder than multiplying or dividing by 100. If it were commonly taught in schools teachers would probably come up with a magical property to make it suitably confusing. No need to come up with a new notation, we've already got an ancient one which would do just fine.