Yeah. When I was still running 5E deadly was the baseline for me as well. Anything less seemed like a waste of time.
Right. But that pressure comes at the end of the adventuring day, not the start. You have to be 3-5 fights in before those resources start to become scarce. That’s where the players sweat and that’s where the fun begins.
I ended up treating named monsters like supervillains. I had a spreadsheet for their stats but let them do whatever made sense in the moment based on their powers. It’s too tedious to make detailed stat blocks. This one controls weather, that one’s a telepathy, the other one’s super-strong, go.
How many encounters between long rests? Sounds like more than the 2-3 you suggested earlier.
To the bolded part, I think that is only true on the DM's side of the screen. I run my games by the adage that, the start of your session should be some of the strongest content. It should be snazzy, dangerous, and set the tone for everything else, and its ok if its the best fight of the night too (so long as the others are good). I try to impress upon my players that they will need to burn some good resources early on, then I'll dip the difficulity of the next 1-2 encounters, and then spike it up.
I usually do 2-4 encounters per long rest; I said 2-3 earlier but 2-4 is closer to accurate. But I usually strive to hit 3-4 specifically; if I do 2, its because its a big climactic battle and I want them to go in full strength so I can have full permission to throw a bunch of insanity for it. These ultra-battles tend to last like 2-3 hours, an entire session for me, but I've ran these for all levels of D&D noobies and have had pretty consistent results But my typical encounter days are 3-4 encounters and all of them are deadly minimum.
If I ever run something other then deadly, its part of a challenge of some sort, or I'm running a very short combat to give my players a win to feel powerful (some of my players have specifically requested this kind of dopamine hit, and I find it important since most of my encounters are so wild). Also, I'll usually do a medium-hard encounter at the VERY start of the campaign to let players get used to their character sheets, kinda' like a tutorial in a video game, and then I'll quickly give them a strong boss early on for similar reasonings, and to set the tone for the rest of the game (don't want them thinking we'll be spending 30 minutes a session fighting something easy).
EDIT: Also +1 to the named monsters as supervillains; I have my named monsters flee all the time, get into skirmishes, etc. Its really fun stuff, and I make a Threat List of all of my antagonists so I can keep up with them. If I have a really good stat block, I usually don't want to use it just once, I want to have fun with it, hence me needing to treat antagonists as semi-recurring instead of always one-offs (though some are one-offs).