I think a better option would be a fee that is triggered off a pattern of undesirable trading patterns over a extended time period (perhaps a year). IE brokerages that has a high percentage of short term trades gets a extra fee, along with customers and funds that do the same. Not preventing a single (or a few) actions.
> you have to hold on to them for a minimum of a week or a month
In general I think that would make momentum stocks much worse, more bubbles and crashes. IE if a stock takes off going up, you will create a bubble anytime you lock out very many sellers. Also locking out sellers in one often locks out buyers in another stock, thus creating more market volatility, as well.
For example as a fundamentals trader I look at a industry that looks promising, and find individual stocks and place a value on it, then look for stocks to give me a chance at a desired return, but expect half of that. For example I might decide I like ag-equipment, and put a values on Cat for $90 and Deere for $85. I buy the one at a better value, if I buy cat at 8am for $85, it is at $90 later in the day, and deere drops to $80 that same day, despite planning to hold cat stock for 2 years to get 10% return, I would take the 5% today in Cat (preventing a price bubble) and instead buy the new better value (Deere in this case.) The point of the market is to keep valuations in check (not too high or too low), so preventing me from selling the Cat stock, and buying the Deere stock hurts the market arbitrage. For example I have had an entire year not selling a single stock, and I have had days where I bought and sold several stocks the same day multiple times. Encouraging people to hold a stock (or houses, businesses...) despite it being overvalued, causes more problems than HFT.