They aren’t recommended due to the stress they put on your back. From Stuart McGill’s textbook, Low Back Disorders:

The traditional sit-up imposes approximately 3,300 N of compression on the spine (Axler and McGill, 1997).

Further, the spine is very flexed during the period of this load (McGill, 1998). The National Institute for Occupational Safety and Health (NIOSH) (1981) in the United States has set the action limit for low back compression at 3,300 N; repetitive loading above this level is linked with higher injury rates in workers, yet this is imposed on the spine with each repetition of the sit-up!

Many recommend performing sit-ups with the knees bent, the theory being that the psoas is realigned to reduce compressive loading, or perhaps the psoas is shortened on the length–tension relationship so that the resulting forces are reduced. After examining both of these ideas, we found them to be untenable.

The psoas does not change its role from a flexor to an extensor as a function of lordosis—this interpretation error occurred from models in which the psoas was represented as a straight-line puller. In fact, the psoas follows the lordotic curve as the lumbar spine flexes and extends. Further, it is true that the psoas is shortened with hip flexion, but its activation level is higher during bent-knee sit-ups (Juker, McGill, Kropf, and Steffen, 1998), not lower as has been previously thought. This is because the hip flexion torque must come from somewhere, and the shortened psoas must contract to higher levels of activation given its compromised length.

Given that the sit-up imposes such a large compression load on the spine, regardless of whether the leg is bent or straight, the issue is not which type of sit-up should be recommended. Rather, sit-ups should not be performed at all by most people. Far better ways exist to preserve the abdominal muscle challenge while imposing lower spine loads. Those who are training for health never need to perform a sit-up; those training for performance may get better results by judiciously incorporating them into their routine.

He also noted that more than one exercise is needed:

Quantitative data have confirmed that no single abdominal exercise challenges all of the abdominal musculature while sparing the back (Axler and McGill, 1997).

Instead, he recommends a set of three core exercises (the so-called “big three”). There are many videos demonstrating the, e.g. here.