We do know for a fact that archery was a much safer choice with far less casualties sustained, usually required training (depending where in the world you are in, sometimes it was a part of life) and was often times seen as a more noble sport than melee competitions. Epics were made to look a certain way and appeal to a certain lifestyle, but it, for the most part, did not represent the majority, who were often melee infantry with some missile weapons such as javelins and/or slings.

Depends on which archer we're taking about too. For example, Arjuna was the archer in a chariot run by Krishna, however chariots were mostly popular in regions of North-west India which have Indo-Persian influences. Terrain is much more flat than the terrain in eastern India, where war elephant with archers on top were more popular due to the terrain and the vegetation and what not. A good example of this would be Asoka's troop balance in historic records and his capital and dynastic roots were based on present day Bihar, on the eastern parts on India. Also there are your typical cavalry archers from northern-middle-eastern influenced heavy cavalry archers to central Asian influenced light skirmishing archers. Most of them have different roles and different training and are not the bulk of any moderate or bigger armies.

Basically I have reason to believe that archery in Indian epics were mostly used to give off a status symbol or a noble vibe. Yes, they were prominent. Effective? I do not know, depends on what archer you're talking about, how, when, why they were used. Like I said, there is a ton. More highly regarded than a swordsman? Regards are often times based on bias, given the fact that the epics came from the thoughts of the educated and the cultured yes, they were far superior according to them.

In reality archers were not the straight forward bow and arrow guys, mostly archers were the minority in any medium to large battle with somewhat specialized roles. Do I really have to break down the word 'swordsman'... cause you're generalizing a lot here.

Your heroes are mostly from Mahabharata where indeed the chariot-borne archer is considered supreme in the battlefield.

In the climactic 18 day battle, most of the damage and action is caused by chariot-based maneuvering and the skill of the charioteer plays a role. I believe this is because it is set (or maybe was originally written) in the time period prior to when cavalry became prominent, but after the chariot was introduced into the subcontinent.

So, even warriors in the story whose primary/favorite weapon is different (Bhima and Duryodhana prefer the mace, and are wrestlers, for example), tend to fight with the bow on a chariot most of the time during the battle.

Other Indian heroes and deities have other favorite weapons (Hanuman -> mace, (goddess) Durga -> Trident, Murugan -> spear, etc).

Source : The Mahabharata by C. Rajagopalachari