When walking on solid, even terrain in good visibility and without imminent danger, most people would naturally use a heel-first strike, as it's a lot more economical in terms of muscle/energy usage. In that sense - if you're looking to build your calves, I have little doubt that consciously walking with a forefoot strike all the time might just do the trick, especially considering that calf muscles have a larger percentage of slow-twitch muscle fibres responding to a larger volume of submaximal loads.
You just have to make sure to take smaller steps, bend your knees a bit more than people generally do and fix your anterior pelvic tilt if you have it so as not to look too awkward (that is, if you care about the social aspect of it.)
When running barefoot or in minimal shoes on a hard surface almost everyone trying to use a heel-strike will quickly and painfully realise what a terrible idea it is and would naturally revert to a fore-/midfoot strike in order to take advantage of the body's natural shock-absorption mechanisms. Only modern thick-soled shoes make heel-first running possible, as they absorb a lot of the shock at the heel so no pain is immediately felt there.
They also make it feel somewhat natural, as when the feet are isolated from the natural ground sensation by centimetres of padding, there's somewhat of an instinct towards a stronger impact to regain that sensation. There's a reason for the extremely high number of nerve endings in the feet. Unfortunately the result is a running mechanic to which we are simply not physically adapted and a huge amount of preventable injuries, which are largely unknown in parts of the world where shoes aren't a big thing.
Feet in the western world are so universally deformed by the continuous usage of modern shoes from a very young age, that I would speculate there aren't many present day podiatrists who've ever seen a healthy real-life foot with naturally spread-out toes and a strong, healthy arch.
Big, strong supportive shoes (especially ones with pointy/compressive toe boxes) are really bad for you, unless you're walking in very dangerous terrain with lots of sharp pointy things, in which case they're great for you. Not the pointy toe boxes, those are always bad for you, but they look better, so you know. Pick your poison.
While biomechanically we're certainly screwed up quite a bit, I would say the solution is retraining according to an intuitive understanding of natural basic movement principles and their application to each specific situation, rather than blindly following a single recipe no matter what.
I don't believe for a second that people walked forefoot-first all the time at any point in human history, although without modern perfectly even roads and thick-soled shoes, they probably did it quite a bit more often. Just check out any video of indigenous people online, they walk heel-first all the time.
Source - lots of personal research, observation, experimentation and some application of common sense. I am not a professional in any related area.