Nope - you're right.
A good way to think about this idea, as well as calculate it, is to tally it up as deltas. Owning 100 shares provides you with 100 delta, meaning that each $1 increase or decrease in the share price will generate $100 change in your value.
A deep ITM call might have a delta of .90, thus purchasing one of these contracts will get you 90 delta.
From what I've seen previously if I go out to the furthest expiration date and look for the option selling for 1/2 of the share price (shares at $900 - I'd be looking for the leap selling for ~$450) then I end up fairly deep ITM and can purchase 2 leaps for the price of 100 shares, and get around .75-.80 delta on the contracts, or 150-160 delta between the 2 contracts.
The key here - are you buying the contracts as share replacements with a bit of leverage, or are you buying the contracts speculating on the future price? All of my thoughts here are in the leap-as-share-replacement category.
Using the option chain at this moment, shares at $890, the 500 strike Jan 2024 call can be purchased for $465. So maybe the 530 strike for $445. The 530 strike has a delta of .8537 - call it .85, so 2 of them will get you the equivalent of 170 shares (counted in deltas). This 2 for 1 exchange doesn't free up any cash though - it just turns it all into leaps that gets you roughly 1.7x leverage.
So maybe you buy 5 contracts to replace 300 shares. That'd get you 5*.85 = 425 delta instead of 300 and leave you with $44k in left over cash. Or maybe go 4 contracts to replace 300 shares, getting you 340 delta (.85*4) to replace 300 delta, and leaving you with $89k in cash left over for other purposes.
You are actually increasing your exposure to moves up in the share price (to the degree that you want to) and getting some cash left over for other purposes.
You are ALSO paying some time value. Those 530 strike calls that you pay $445 premium for is the equivalent of buying shares at $975, or $85 over the price available today. THink of that $85 in time value as the interest you pay on the loan to own 170 shares using the cash that would purchase 100 shares. You can recoup that $85 in time value via covered call sales if you'd like. Or you'll come out ahead when the shares go up past $975.
You can (will) also roll or sell these calls well before expiration. Say 3-6 months? Somewhere around there you'll find that around 1/2 of the time value is gone. Which also means that you can recover half of that time value that you paid up front.
You might also find that the shares have gone up so much that the time value is down to roughly 0, so you might as well hold to expiration, and you won't care in the slightest that you paid $85 for the privilege (you'll be pretty excited in fact).
You can be more ATM as you mention. The leaps are less share replacement in that case and more speculative, but this stuff is all on a continuum anyway. I got deep ITM on my purchases to minimize the amount of time value I'm paying for, as well as better enabling sales of covered calls.