I use Henson as my guide post. If you don't push yourself, you don't get better. When it comes to cost, I've always felt that people will pay for things of quality, but there is also a real beauty in making "the best thing at a certain price point" (if that's your goal).
I'd take that a step further and say that being forced to work within certain boundaries will force an artist to become more creative. I've heard of strange exercises where an author will write an entire story, sometimes even a novel, by starting every word with a particular (common!) letter, or by excluding a letter from any word he writes. People have done so well at it that some of these works have been published.
It's not much different from, for example, forcing an artist to work within a budgetary restriction or to create a great piece of artwork that fits on the outside of a tuck box when it's folded and glued.
I'd even wager that Jim Henson had to work within similar restrictions when he created the Muppets - the name is a portmanteau of "marionette" and "puppet". He created them in the early 1970s for a new children's show on public television called "Sesame Street". I remember from that era that public funding for anything was hard to come by, so their budgets must have been miniscule - the main set of the street got used a LOT, and many if not most of the rest of the scenes were played against a blank background wall with a shorter wall nearby that the Muppets often sat on, in order to hide their Muppeteers. In dreaming up a way to portray the "creature" characters, they wanted to find a solution that could give them the physical control and speed of movement that a hand puppet had, while at the same time developing some means by which to move their limbs, just as a marionette does, in ways that a normal puppet simply couldn't replicate.
Anything that even resembled a special effects budget was out of the question - most movie and TV studios had ditched whatever special effects departments they had back in the 1960s. So they had to come up with something that was not simply effective, but also cheap. So they stitched together some hand puppets with rigid, jointed limbs, attached nigh-invisibly thin, straight poles to the wrists and devised a way to control the mouth and face with one hand and the limb movements with the other. It actually borrows from Asian traditional shadow puppets, but allows for much better visual impact with the use of color and movement in three dimensions.
My point being, there must have been countless little restrictions and obstacles that they needed to overcome in order to make the Muppets work as believable characters, but they found a way and made an entertainment empire out of it...which is now just another branch of the Disney Company! But on a serious note, consider this - would Henson have been so inspired, had he the budget to use something different, like animation, animatronics or some other blow-the-budget kind of solution? Would the Muppets even exist today were it not for the budgetary and other restrictions he had to work with on Sesame Street?
Wow, uh, sorry about the wicked-long tangent...