First of I haven't seen Rose play this season, so things might have changed.
I see him as a bit too similar to Walker, they feel like the prototypical face up players were they are great when facing forward and have space to run into, but they struggle when in tight spaces were better technical ability is needed.
We need one fullback to be more like BAE (not necessarily him) with good passing and the ability to keep the ball within the team even when put under pressure. Not so much this year, were BAE has had a weak year, but the last few years Benny's distribution has been absolutely crucial to our success. If we want to play possession based fotball we need a player with good technique and passing ability at left back.
Maybe Rose has developed into this player, but I strongly doubt it.
I'm not sure how true that is.
You talk of needing a good passer at left back and how it has been crucial in recent years, however during those years we played almost strictly a central 2 in a 4-4-2 or 4-4-1-1. Moving to a 4-3-3 would do a few things in relation to Rose. Firstly it would allow the extra midfielder (Sandro) to drop deep into the defence, allowing the central defenders to play wider (both Verts and Kaboul have played full-back on their respective sides). At the other end of the pitch, with 1 less player in the centre, the wide players have more of a duty to get close to the central striker, both by staying high up the pitch (also pinning back the opposing full-back), and cutting inside for efforts on goal (this also would suit Bale).
So, in the opposition half there would be more space for the full-backs to attack due to a) the higher positioning of the wingers and b) them cutting inside, which you admitted suits the playing style of Walker and Rose. Meanwhile while one full-back raids, the other can retreat and as Sandro drops into CB, one CB becomes a full-back and the back 4 can be maintained.
While this formation is more suited to the full-backs' ability to run into space, it alone would not account for their lack of composure/creativity in possession (although Walker has produced the occasional sublime pass this season). However, with the signing of a creative midfielder, the simple presence of a third man in CM and the increased central responsibility of the wingers we would not need a particularly great passer at LB. Often BAE would go straight to Adebayor, but in such a system the LCM/CDM would take creative responsibility from the LB and the WF could drop into more central spaces between the lines, offering shorter passing options than Adebayor (requiring less passing precision/range, a point compounded by the full-backs' higher positioning).
Also part of the reason BAE's passing was more crucial in past seasons than 12/13 was because Bale played at LM and was one of our most lethal threats along with Modric who played LCM, so this was the passing hub of our team in deep areas. The trio dovetailed nicely, but now both the squad and Bale are moving away from the sort of system attuned to BAE's skillset. Bale is moving higher up the pitch, and following this summer I believe our squad will be more suited to a full-back providing a direct attacking threat who can overlap and hit the byline (a la Walker) rather than a slick passer.
However, it might be safe to have one of each as an option, especially to see out tight games with possession. In an ideal world we would sign ourselves a young Jordi Alba, keep BAE and Rose as back-up and sell Naughton. However LB is probably 4th on the list of priorities this summer behind ST, WF and CM. I could live with BAE, Rose and Naughton as our left back options next year if we got good players in the other positions. Give Rose the chance to fight it out for a first team place in a system that suits him. It would be nice to replace Naughton with another young, more attacking, left footed LB and use him strictly as a right-back if we had the money (also then hopefully we wouldn't be forced to play Verts at LB).