Arihant size does influence the article it can launch but the conscious choice for some IRBM class SLBM show it is planned rather than a forced decision. Not sure many, if any IRBM class slbm is in service by the nations that operate ssbn. Without knowing the arihant silo dia, we can not tell even why it was made that way. But it is likely how we have progressively built our capability. So a submarine purpose article was derived from the Agni 4 class first stage , both A1P and A4 have same dia 1.2m , that for submarine use evolved into a 1.4m stage booster-sustainer stage. Similarly the 2m dia class A3 A5 now get translated into 2.4m dia SLBM K5. We could easily have built K5 with same A5 characteristics for easier weapon system integration, but it did not happen.
Next up, we have the new shell being made to be proven, the 3m dia class massive slbm likely K6 with very large payload. If it is proven then S5 will also deploy its goodies in similar fashion like arihant did with k15 and k4.
K4 being very slim comparatively can not sustain deep underwater launch with a heavy payload on top, the transition from water to air would not be as smooth without that nose mounted tractor puller mechanism. After all we have to acknowledge the restriction it has, something A5 like article can survive pushing thru water from a deep position, but a slimmer K4 will have problem both unilaterally pushing thru from 30-40m deep or quick push thru like K15 similar to a brahmos underwater launch, esp with a 2 ton class payload. This is self imposed design choice. In this regard the ejectable nosecap use means K4 is able for both a high payload delivery and a depressed trajectory based flight profile, it can fly like k15 in similar fashion for a shorter haul.
The VLS dimension is not that severely restricted imo. You need to know the gas dynamics inside the tube, the tolerance limit of the seal and force on the end rings that hold vls upright in silo. These parts are needed to be very precision make with high shelf life, with zero error tolerance so the sub itself is not affected & able to absorb the shock & vibration via the shock absorber mechanism in place.