She might be able to run sub-60, but not by very much. If she truly wants to remain as a 1500m runner (moving up from making the final at USOT in 2008 to becoming a medalist/making a national team in the event in 2016) she does have to get faster over 400/800m (if possible). Otherwise the distance races (5000,10000 and Marathon) will be beckoning.
To truly be a sub-4 1500m runner with any consistency, running under 2.00 for 800m is a requirement. Suzy Favor and Mary Decker could run 1.58/1.56 to run 3.57. For a distance type (which she is), 2x your 800m time = 1500m time, is a bout right. 2.08 x 2 = 4.16 (she has run 4.14?, so was likely able to run about 2.07 at her peak then).
For that matter, Sheila Reid has to do the same (even if she has a pretty good kick) in order to be a player on the world 1500m scene, and not just NCAA's. Olympic A standard is about 4.06, so 2.03 seems reasonable to run that or faster, with GOOD endurance (i.e. also being able to run about 8.45 for 3000m). Steph Twell (UK - same age as Reid) has run 58.1, 2.02+, 4.02+, 8.42, 14.54 on the track (plus road times of 53 minutes and sub-1h12 for 10miles/half Marathon). This shows her endurance capacity (and likely the volume of aerobic work, either in mileage and/or Intervals).