OP seems to be based in SFO and flying to LAX, rather than vice versa. Since no rental companies or public transit is within walking distance of T1, I don't thinki this difference is as big for those arriving in LAX (for them, on arrival, T1 is the furthest from the exit) as those of us who are local to LAX and either park at PNF's Park One (where T1 is about a 3 or 4 minute walk away from self-parking spaces to the right as you enter from Century) or take the Culver City bus that stops outside of Park One on Sepulveda (where it may be a minute or two longer, but the point is you walk to and from T1 in both directions).

(If I don't park at Park One, I feel the advantage of T1 over T4 evaporates in the long run, because I have to use a shuttle both ways anyhow.)

And, btw, if the OP has no status at WN, then security lines for most people are so much longer at T1 than the Priority Access lines (especially if you're signed up for PreCheck) at T4, that that more than offsets the shorter time in the shuttle on arrival. I still get past security faster, coming in on a shuttle, at T4 with the same status the OP has, than at T1 but with no status.