Shouldn't the theta also go down with gamma as we increase DTE?
100% no. Think about it like this: An option has 100$ premium and 20 DTE. We now asume theta is linear (which it isn't but...you know, simplicity)
You collect 5$ per day.
If the option has 200$ premium you get 10$ per day, makes sense? Now what about gamma?
Think about a 100$ strike option that has 20 DTE and it's premium is only 2 cts. The stock is moving 1$ per day average. Meaning on a single day, the option could either have a delta of 1 or 0 at the end of each day. Your gamma is insanely high but you only collect 2cts over the next 20 days -> your theta is tiny.
Now if the 100$ strike option is worth 200$ premium (which is absurd for a 100$ stock, but...simplicity), at the end of the day the option delta is still 0.5 but you collect 10$ theta for that...per day. Gamma is basically zero
The important factor is the theta/gamma ratio: How much do I lose when the stock moves vs. how much do I get for it in decay.
The driving force is implied volatility. The higher implied vol, the better the theta/gamma ratio.
If you compare different maturities, you want to look at this ratio. Theta goes down with DTE since you have to wait longer to realize the premium but gamma is even lower.
When you trade calendars you want to capture curve rolldown. Meaning if front is lower than backmonth, you want to buy front month and sell backmonth. You buy cheap gamma, because IV low-> theta/gamma is better for the buyer and you sell expensive theta because IV high, theta/gamma is better for the seller.
Plus if 30 DTE is at 20 vols, 60 DTE 30 vols and 90 DTE 40 vols and you sell the 60/90 calendar, you buy 30 vols and sell 40 vols. As 30 days pass, your 60 DTE will now be 30 DTE so you lost 10 vols but you made 10 vols as the 90 DTE becomes 60 DTE. As the longer dated option has more vega, you win here, too.
BUT you're short vol and that's your risk.
When you look at what the majority of retail is doing with calendars: They wait until market does not move - which makes the front trade lower than the backmonth.
Then they sell cheap front month theta and buy expensive backmonth gamma.
In extreme situations you are short gamma and get zero theta for that, plus you're long vol and short rolldown. Not very smart