Are you concerned about the sticky grease attracting and holding dust and silica and anything else that could wear at the springs?
Would it be better to use a lighter oil, like CLP, that leaves a thinner film?
I do not believe so. I think products like CLP are great for their purpose, but not good choices for lubricating folding knives. Lighter oils are commonly used on knives, but I don't think they are ideal for folding knives because of the constricted movement that results in contact friction, which ultimately results in wear, plus a tendency for a liquid oil to not stay put on certain parts of a knife. While most folding knives now use a washer system that uses a material softer than steel (bronze, teflon, film, etc.), almost all folding knives still have points in which you have steel-on-steel contact (generally a hard stainless steel with the liner, and a harder stainless steel or tool steel with the blade), and this is especially true with AXIS. I am a strong believer that with the omega springs (and with most of AXIS, and with most all of folding knives), a lubricant that favors reducing friction (hence wear from repetitive contact) is by far the best choice, and this is almost never a liquid.
Many newer greases reduce the dirt buildup you mentioned greatly over greases from years past, while simultaneously providing better initial lubrication, a better operating range of temps, greater resistance to removal from water or other liquids, and great resistance to migration (a HUGE issue with knives). The actual grease used would determine how good (or not good) it is. While something like RIG grease would be less-than-desirable, I would argue that a fluoropolymer/fluorinated grease is the best choice for this sort of application.
I believe the reasons that Chris Reeve includes and sells a fluorinated grease with all of their folding knives are simple: ease of correct quantity application, smoother operation, longer maintenance intervals between reapplication, decreased fouling/gunk buildup, decreased wear, and improved service lives. Given Chris Reeve is widely held to be one of the or even THE authority when it comes to folding knives, I believe his decision on fluorinated grease confirms the suitability of this product for folders.
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Unfortunately, this is going to get more complicated. Sometimes, companies advocate lubricants without recognizing just how poor them perform. For a long time, Benchmade strongly advocated Militec-1, for reasons I will NEVER understand. Militec-1 is perhaps the worst lubricant ever made...it's complete crap and in many cases, worse than no oil at all!
It has consistently failed government testing standards, has been proven to increase corrosion on metal over untreated, provides no actual lubrication in its wet or dry form, and the company blames independent testers for why their product performs poorly rather than improving their crap product. It is 100% snake oil. It has probably cost Benchmade money because it is useless for lubrication, encourages corrosion, and hence has probably
accelerated wear on the omega springs. As Benchmade is an excellent company and one I associate with 100% integrity and 100% quality, I do not understand why they would associate themselves with that sleezeball company like Militec or use a lubricant that lowers the bar. Still, this shows that sometimes the right lubricant is not as easy to identify, and why forums like BITOG and extensive independent testing are now huuuuuuuuge.
I often here people say that any lubricant will work and that the difference isn't all that great. I could not disagree more.