By the XVIII century the remaining (Peter the Great curbed them down a bit...) streltsy were musket troops some of whom did carry bardiches, pikes, etc; similar to western european musket units of the time (eg. exclusively pike units were not common at the time; more common were mixed musket - pike units).
But never mind that, could you imagine a unit NAMED "longbowmen" in English (for example) carrying only bills? "Streltsy" means "shooters" in Russian. It's as simple as that.
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