Portfolio optimization techniques are used quite a bit by hedge funds. I think you misunderstand how portfolio optimization operates in the context of an active trading strategy. Your question suggests a view of portfolio optimization as a tool to adjust portfolio weights arrived at by a separate, active strategy. Under that approach, you are correct, the weights would no longer be optimal if the active strategies are allowed to turn positions over without any re-optimization of weights.
However, there is nothing stopping funds from optimizing their portfolio daily and even intra-day. Also rather than thinking of the trading strategy and portfolio optimizer as distinct systems, consider these as a single, integrated system. The "trading strategies" are really just E(R) (in your symbology). If the view on a stock changes then E(R) changes and the portfolio can be re-optimized to reflect this change. This way, the portfolio optimization is the source of the trade rather than something tacked on afterwards. The more often E(R) change significantly, the more "active" the strategy is.
There is a substantial literature describing portfolio optimization techniques intended for active management. This paper is a nice place to start. The distinguishing characteristic of these approaches is that they account for transaction costs. Absent costs, it is adequate to just compute optimal weights whenever an input changes using standard techniques. Accounting for costs requires us to model how the weights are changing in time, which standard techniques do not address. I also suggest you take a look at the optimal execution literature, as there is much overlap.
Although many funds do use portfolio optimization with active strategies, there are various reasons why some funds choose not to. Some lack the specialized expertise to formulate and solve the relevant problems quickly and reliably. Many funds reason that finding accurate return forecasts is more important than portfolio risks and so focus their resources on the former. It can also be difficult to get portfolio managers and traders to accept a single optimized solution as they often prefer to have control over their own positions. Lastly and perhaps most importantly, portfolio optimization has a definite stigma attached to it by the practitioner community. I believe the oft committed mistake is in thinking of portfolio optimization as a "turn the crank" procedure rather than as certain general ideas that usually need to be carefully applied to the specific problem domain.