B737-700 Captain reported encountering strong wake turbulence departing LAX in trail of a B757; and recommended increased separation behind B757 and similar aircraft types.

Narrative

Last leg of the day. We were full with one jumpseater in the flight deck. We taxied out to 24L. Ground Control put us behind a 757 in the line up. I used to be more concerned about wake turbulence behind a 757; but not so much now since the changes in separation behind 757s. In the old days; I would have just done a max thrust takeoff to reduce the chance of a wake turbulence encounter (it took about two seconds to do it). For us to do a last minute change now; we would have to send for new takeoff data; and run a Departure Checklist. I was tired and didn't think it justified it. I knew the Tower wouldn't appreciate the delay either. Since the FAA decided the wake turbulence of a 757 was not a problem for my 737; I didn't see a threat. Once the 757 departed; the Tower cleared us for takeoff. At 200 ft. AGL; we encountered the 757s wake turbulence. It was more than we anticipated. At multiple times; our aircraft was abruptly rolled to the right by the wake. I saw the FO (First Officer) counteract with full left aileron; even as the aircraft continued to roll right to 25 to 30 degrees of bank. This went back and forth as the ailerons became effective; then not so effective. At 1000 ft. AGL; Departure Control gave us a vector off the SID; and then we were out of the wake. Both the FO and I were very surprised how strong the wake was (and how ineffective the ailerons were at times while in it). The first thing I'll do [in the future] is to request a delay for takeoff from Tower; when departing behind a 757. I've heard guys ask for delays for this reason before; and Tower has not responded very well. It sounded like a huge inconvenience for them (Tower). The next thing I'll do is be more proactive in doing a max thrust takeoff. I think the FAA needs to add more separation between 757s and 737s (or similar). This IS a threat and needs to be addressed.