Easy-Kill, thank you for your informative post.
I think another indicator that infantry melee wasn't that important was that infantry stopped using armor of any kind. They did not wear padded or leather armor nor any kind of helmet, while before almost any infantry wore at least some armor. Cavalry continued to wear armor, mostly breastplates and open-faced helmets.
The above image is a Pikeman's Armour from J Bingham, Tactics of Aelian, 1616. However General George Monck, wrote 'Observations upon Military & Political Affairs: The formost English handbook of Generalship and Statecraft', during his imprisonment in 1644-1646((Published in 1671). Within the chapter looking at The Defensive Arms of a Pikeman he recommends that a Pikeman should have 'an Head-piece with Back and Breast'; he also recommended that the Pikeman wear 'a Buff Girdle of double buff 8 inches broad, the which is to be worn under the skirts of his Doublet instead of Tassets'. This was principally motivated by weight; one of the upshots of the English Civil war was a move away from the relatively static siege warfare of previous generations and a transition to 'decisive battle' and low level skirmish warfare.
Incidentally, the armour was designed to withstand pistol shot.
If bayonets and other melee weapons were a significant threat, people would want to wear armor. However, I think musket-fire and later one artillery-fire were such dominant threats, against which armor did little, infantry ditched all armor. For cavalry, melee was still very important and thus armor was retained.
It should be noted that Monck's observations are probably the ideal. Furthermore, most of the English commanders would have been trained and influenced in the Dutch and Swedish forms of warfare, and heavily favoured Armour for Pikemen. Once the English Civil War broke out, the Royalists found themselves without access to the Armouries of London and Hull. The first stages saw the acquisition of arms and armour, principally by the trained band militias (who were expected to own their own armour). Nevertheless, In 1642, Parliament placed an order for 6000 pikes and 6000 'corslets'.
There is supposedly no record for any acquisition of pikeman armour for the New Model Army, though it is highly likely that as the fraction of pikemen reduced, existing armour was sufficient to supply them. There are many many records for the acquisition of clothing, particularly the red coloured jackets that would become synonymous with the British Army. However, William Lockheart wrote to
People might counter that armor was expensive and that was a more important reason for infantry ceasing to use armor. That might be true, but I do not think that's the complete picture. Against melee weapons, even light armor like a leather coat is really helpful. Padded and leather armor isn't that expensive.
Professional officers like George Monck and William Lockheart regarded infantry armour as essential, even when the ratio to Musketeers was decreasing. For example, William Lockheart commanding the New Model Army serving as allies to the French in 1658 asked John Thurloe for 1500 corslets (and received 500 from the armoury in the tower of London). His reasoning was that it encouraged his own men and that 'a stand of 500 pickets well armed with headpiece and corslett will be a very terrible thing to be seen in these countries.' It should be noted that it is highly likely that only the first ranks were 'armoured' and that practicalities.
As for the cost, a full set of infantry armour cost 1#2s , while a pike cost between 3s10d and 4s2d (when delivered to Thomas Fairfax's army (again the Mungeam contracts). Not including the other clothing/arms which was common to both Pikemen and Musketeers, this was a total of about 310d (pence). Compare this to musket and Bandelier which cost about (160d). The cost is not that dissimilar and if you consider that you have 2 musketeers to every pikeman, the cost for both is about the same.