I thought that buybacks reduced the amount of shares in total, increasing the value of the remaining shares?

The value of the shares is not increased when the buyback is made. The total value of the shares goes down, as they would have if a dividend was paid. The total value of the shares will go up in the future, as it would if a dividend was paid. The value per share will grow more than in the dividends case, as there will be less shares, but of course an investor who kept all their shares won’t have received any cash (unlike in the dividends case).