Why do the 737-100's JT8Ds, and no others, have suck-in doors?
Since the production of the 737-100 and -200 was concurrent, there were in fact -200s with blow-in doors, and more often than not, the inlet was replaced during the airframe's lifetime. An example is United's N9003U, line number 12, a 737-200:


Sources: jetphotos.com and airliners.net

The doors are spring-loaded and open by differential pressure at medium-to-high thrust settings and slow speeds, i.e. during takeoff and landing, i.e. near communities. The openings created in the inlet allows the inlet noise to escape, which is a major source of noise.
Therefore, and evidently, both manufacturers and customers have favored the sound-absorbing inlets.

(...) the noisiest test configuration had an inlet duct with simulated blow-in doors. When the blow-in-door inlet was installed, the A-weighted sound power levels were approximately two decibels greater than when the inlet with no blow-in doors was installed.[1]


An additional design feature for minimum noise is the use of a single opening inlet at all operating conditions. The use of devices such as blow-in doors to bring additional air into the engine at some engine powers has some aerodynamic advantages but increases engine noise. No blow-in door systems are in use on the DC-10.[2]

From a regulatory aspect, at least in the 747's case – which sported those inlets in its early days – the noise-aimed regulations of the 70s were the reason for their replacement:

After promulgation of FAR Part 36 and application to the 747, substantial changes were required for the engine installation. The blow-in-door inlet was replaced with a fixed lip inlet providing a large reduction of the fan source noise while the surface area of the acoustic lining contained in the engine and nacelle was more than doubled.[3]


1: Marsh, Alan H., Robert L. Chapkis, and Gary L. Blankenship. Study of Noise-Certification Standards for Aircraft Engines. Volume 3. Selection and Evaluation of Engine-Noise-Certification Concept. DYTEC ENGINEERING INC LONG BEACH CA, 1983.
2: McPike, A. L. &quot;Community Noise Levels of the DC-10 Aircraft.&quot; Journal of Aircraft 9.8 (1972): 542-547.
3: Little, J. W., and R. E. Russell. &quot;Status Report: Subsonic Aircraft Noise Reduction.&quot; Turbo Expo: Power for Land, Sea, and Air. Vol. 79757. American Society of Mechanical Engineers, 1976.