Unless the spindle is marked cro-mo or something to that effect, it's possible that it's just case hardened and made out of a lower quality steel.
A lot of Japanese spindles were made that way, especially Sugino Maxi style spindles with end nuts instead of bolts. The dark areas on these hardness test specimens show the depth of the case hardened surfaces which range from ~.005" (0.127mm) to ~.050" (1.27mm) deep.
They're about 60 Rc on the surface while the center can be a lot softer.
The size of through holes in BB spindles is ~7mm. The spindle is probably 110mm - 116mm long. The hole depth is 16 to 16.5 times the drill diameter deep.
Standard style drills going that deep tend to wander off center so the drill could come out the other side as much as 2mm off the center line, weakening one side of the spindle. Also removing chips from a hole becomes a problem.
There's a possibility that the drill can grab and break too.
Back in the 1970's most bicycle components were machined on old low tech equipment. Older and/or less expensive spindles were drilled from both sides leaving a mismatch in the middle.
High quality spindles were/are machined on modern CNC equipment with high performance drills.
Here's a neat example, this is a 9/16" (14.27mm) high performance carbide drill going 4.5" (114mm) deep in 28Rc 4140 alloy steel.
Total drilling time 6 second! When this video was made that drill had already done 3500 holes!
https://www.youtube.com/watch?v=-E4te5stFmg
PS. I'm involved with these products.
My recommendation is get a hollow axle that fits your BB if that's important to you.

You'll be hours ahead and not have to be concerned about spindle breakage... (think Fignon)
But... who am I to discourage someone from experiencing the pleasure of working with your hands. I still like to fix or modify bike goodies. When possible safety issues are a stake, that's when I butt in with my 2 centimes worth...
verktyg
Chas.