I can absolutely believe that, and especially of Charles I who spent a lot of money on image-maintenance through statement pieces such as art collections and ships. It seems that in the early modern period the essential penis-extensions were a massive artillery train and/or a massive warship. The early Ottomans built some unjustifiably huge cannon which proved a nightmare because they were too big to move. During the member-measuring between Henry VIII and his northern neighbours, Scotland maintained one of Europe's most impressive artillery parks, which saw hardly any action, as well as making a play for the "biggest ship" title with the Michael.
If you could combine the two and have a massive warship rammed to the gills with artillery then so much the better. Indeed one of the factors in the buildup to that war (as you are probably aware) was collection of "ship money", much of which went towards construction of the Sovereign of the Seas, which apart from its massive tonnage was covered in enough gilt to do justice to a small palace.
Though at least the Sovereign was an effective warship if an unnecessarily expensive one. The reconfigured and overgunned Mary Rose was a famous failure, and the Vasa didn't even make it out of the harbour on its maiden voyage before sinking.
The rock-paper-scissors interaction between infantry, cavalry and artillery was definitely a thing, but only really came into its own during the 18th century. Napoleonic gunnery was much, much better than during the Thirty Years War, which was partly because of improvements in the guns themselves (and to their ammunition) but also because of general improvements to understanding of mathematics, leading to better training of the gunners themselves.
During the English Civil War, at least, artillery do not seem to have been particularly effective outside sieges. The only major contribution I can think of artillery making to a field engagement was at Lansdowne, where Waller's bombardment of Hopton's march provoked the battle. Hopton's troops then promptly stormed up the hill and took the position despite Waller's artillery being well-set.
The Swedes did manage to make effective use of it, but they were also the best army of their era, and Torstensson was an unusually talented artillery commander. It might be that his success encouraged other armies to persist with their own artillery even where it wasn't really making much practical difference.
It must be admitted that the quality of troops in the English Civil War* was not for the most part particularly high until the later stages. Many of the officers were excellent, having served in Dutch or Swedish armies, but the soldiery were mostly levies, and it frequently showed. There is an infamous account of a cavalry troop being wholly routed by a field of runner beans. Where troops had been properly drilled, like the Cornish trained bands who joined Hopton, the gulf in quality between them and their opponents was often remarkable.
So it's likely that Civil War armies did not make the best use of the artillery available. Even if they did adopt Swedish tactics (and Rupert in particular was a big proponent of them), the Swedish system relied quite heavily on the troops themselves being disciplined and experienced. The tendency of royalist cavalry to rout their opponents and then hare off all over the place rather than regroup to support infantry is well-known. Similarly, it's been suggested as a factor in the stalemate at Edgehill that the adoption of the on-paper superior Swedish system by the royalist infantry in fact handicapped them, because the troops weren't good enough to make proper use of it and it just led to confusion. I'd be surprised if artillery didn't suffer from the same handicaps.
*no offence to Scottish, Welsh or Irish theatres intended