Historical equities compound growth almost entirely comes from constantly reinvesting dividends to buy more shares which compounds to increase future dividends. So as an example, take a company that returns 5% of their share price and an investor pays a 20% tax rate allowing them to reinvest 4% after tax money to buy more shares. After 40 years, they'd have 1.04^40=4.8 times the proportion of the company. If the same company spent all of its money buying back shares, you'd have 1.05^40=7.039 times the company. Now you still have to pay that 20% on gains once you sell so after you'd have (1.05^40-1)*.8+1=5.83 after selling but that is still a 21% benefit for share buybacks in that example.
Also, I wouldn't call that "artificially inflate the stock price". They are reducing the number of outstanding shares thereby increasing the earnings per share which increases the amount that can be returned to each share such as through higher dividends. It is effectively reinvesting the dividends for you back into the company.
