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Isn't the downside to selling covered calls that, not only do you need to hold the underlying, you can get the option you sold exercised, aka you lose your 100 shares per contract?

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Yes, so the upside is capped but you get to set the cap based on what call you sell. The bet you're making is that the stock won't appreciate enough for the other party to exercise the call option (so you earn the option premium + underlying appreciation). If the option is exercised you lose some of the gains you would otherwise have made, but you still captured some of the appreciation.

But there is no increase in downside in the financial sense (if the stock price declines you keep the premium).

but if I hold the underlying long in the first place, I’m bullish in it, and I don’t want my shares to be “called/exercised” away from me, no?

Yes, but you might think it will appreciate less than other people do and expect to make money by selling calls on average.

You can technically do it with buying future of a stock and selling covered calls.

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