|Your idea about "trading a small percentage of the shares" to determine valuation of all shares is not precise enough.|
What really matters is not the total number of shares traded but the kinds of trades and their influence on price. a perfect market system requires large numbers of relatively small size trades such that no single trade can by itself cause the price to change.
An example: If the average daily trading volume for QCOM is about 16 million shares, and if a single entity (e.g., hedge fund, trading firm, etc.) trades, say, 2 million of those average 16 million shares for the day, you can take it for granted that the actions of the trading entity did have a significant impact on the price of the shares. Even if individual trades are only 1000 or so shares, if those trades are initiated by a trading program set to buy or sell 1000 individual trades in a matter of seconds, there will be an impact on share price. That is an abuse of the market system.
Which is why we need a disincentive to make these quick trades that make it impossible for all those in the market for a given stock to be on a level playing field. There is no better equalizer than a service charge that penalizes quick trades, while at the same time offering an incentive to lower taxes on long term trades.