In US football...what is an "eligible receiver" and why not declare it every play?

I don’t think I’ve ever heard a referee announce it, but the stadium announcer definitely does.

I would bet you’re right because the vast majority of field goals and extra points would want o linemen as ends for blocking purposes.

The usual tackle-eligible play is either intended to be a subtle shift in where the wide receivers line up, thereby leaving the weak side tackle eligible, or as part of a unorthodox formation that defenses haven’t trained against.

Either way, having to publicly call out eligibility kind of removes the point because having a non-standard player eligible is part of the misdirection.

They only need to tell the opposing team about it, and since they are there on the field with them it shouldn’t be necessary to do it over the stadium loudspeakers.

If you watch a field goal or punt, not everyone is on the LOS - there are 2 or 3 guys a yard or so back from the line, so they can pick up anyone who makes it through the front 7. Look at this video from the Ravens field goal to beat the Cowboys - the 2 guys in the backfield are 95 - Tavius Robinson OLB, and 93 - Calais Cambell, DL.
video

One of the reasons why I really like football is all of these subtle things that seem inconsequential, but in reality can make a big difference and are part of the game strategy. But it’s also okay if you don’t know about them and/or ignore them, because you can enjoy the game just fine without it. There is a lot of depth to the game, but that depth isn’t required to be a fan.

(Remembering all the weird and sometimes contradictory rules, on the other hand, is probably not fun for anyone, including players and even officials.)

Which they have to be, by the rules. Kicking plays from scrimmage (PATs, field goals, and punts) must follow the same formation rules as regular scrimmage plays: 7 players on the line of scrimmage, with the two “ends” being eligible receivers, and 4 players behind the line of scrimmage.

On a field goal/PAT, two of those four are the holder and kicker, but the other two are blockers who start the play in the backfield, as you note.