Is headfirst sliding to first base really slow? [baseball]

Consider whether the common belief in baseball that first base is faster when you run through it is true.
From reference (2), the speed is further increased by the step just before headfirst sliding.
It looks like it could be more advantageous.
So choose a course of action that is worth the risk.
References.
How to Slide Your Headfirst for a Faster Base Touch than Running Through," Hiroshi Shimomura
Diving Into First Base: Maybe Not Crazy (Ref #2)
blogs.fangraph...
Ritsumeikan University Analysis Reveals Baseball's Popular Theory about Reaching First Base Faster Than Head Start (Reference 1)
www.kyoto-np.c...
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