Just like you I swing trade and don't day trade so I am on your side, but I think your logic against compounding with day trading is a little weak. Unless a day trader keeps taking money out, and assuming he is net positive, his compounding is as valid as ours.If your profits from previous days are reinvested and you end up making profits going forward than yea, that would be compounding. However, you have 2 take into account trading costs which in day trading can be significant, your also faced with having to always buy in at higher prices for longs in a bull or at lower prices for shorts in a bear market which makes it harder when you have to get re-positioned into a new winner every day.
As a swing trader: When I have compounding I have a static cost basis, I also get the benefits of overnight gaps in my trade direction which can add considerable profits over the weeks/months. Compounding has a way of working a lot better when left alone letting a profit in motion continue to churn more profits.
When I day traded for a living (6 years, mid - late 90's) my trading costs were as much as $45k. On wining years it was transparent - on flat or losing years it was tragic - you don't get any compounding until you first overcome the trading costs. Investors benefit the most from compounding - us more active traders are typically well outgunned by this crown in a raging bull market.
The high cost of day trading on the other hand is valid because of large accumulation of commissions with a large number of trades.
Regards,