In comparison to an early grant a refresher grant will be smaller and worth less, but that doesn't make it "near" worthless.
First, if you have 7 years to decide if you want to exercise it, then every stock option has risk-free upside regardless of the strike price. Without the 7-year rule then the upside isn't so clear cut, but that doesn't mean they are near worthless at all.
Second, companies really don't grow that quickly. Over a 1 or 2 year time horizon, even a really successful company will 2x-4x in value (and the common stock might grow even less than this). If the strike price was low on the original grant, the strike price will also probably be pretty low on the refresher grant. Especially at early stages of a company's life when the options are priced at essentially zero, even if you 5 or 10x the value, the strike price will still be very low.
When you have more established companies and higher strikes prices, it is less of an issue because there might be a shorter term path to liquidity which takes away risk of exercising without being able to sell the stock.
The dramatic difference in price is really between pre-funding to post-funding. e.g. I know many companies where options were granted at 1c a piece, even as seed notes and safes were given out, but as soon as the Series A equity round hits, the 409A & thus options grant went up to $0.50+. That's a huge difference.
That said, your point about having 7 years to decide is entirely fair, and mostly negates that downside.
First, if you have 7 years to decide if you want to exercise it, then every stock option has risk-free upside regardless of the strike price. Without the 7-year rule then the upside isn't so clear cut, but that doesn't mean they are near worthless at all.
Second, companies really don't grow that quickly. Over a 1 or 2 year time horizon, even a really successful company will 2x-4x in value (and the common stock might grow even less than this). If the strike price was low on the original grant, the strike price will also probably be pretty low on the refresher grant. Especially at early stages of a company's life when the options are priced at essentially zero, even if you 5 or 10x the value, the strike price will still be very low.
When you have more established companies and higher strikes prices, it is less of an issue because there might be a shorter term path to liquidity which takes away risk of exercising without being able to sell the stock.