Tmoose... Hmmmm...
In Your attachment, the table/flag notes [extracted from ASTM A29 Standard Specification for General Requirements for Steel Bars, Carbon and Alloy, Hot-Wrought] discussed most of the trace elements you mentioned... but with an over-arching statement, roughly.... 'xx to be as specified by customer and agreed by vendor/supplier'...
Since You are discussing typical/standard commercial carbon steels [A26] there should be a very important MATERIALS purpose for specifying 'clean carbon steel' in the procurement... with the added burden of cost/schedule for purity, analysis and certification.... ‘as specified by customer and agreed by the supplier’. Otherwise You can get [barely] what the base spec allows on delivery. Perhaps an aerospace grade would be a wiser choice than a commercial grade.
IF trace elements could have an important affect on Your product, then You have to specify elemental limits as part of the contract with a reputable supplier.
An old aerospace fastener/materials engineer once told me... and I have never forgotten... “You deserve to get what you ask for: but if You don’t ask for very much, don’t-expect to get very much.” --R. Nelson, XXXXXX engineer.
Or... as TheTick phrased that same sentiment this way... “You don't get what you want. You get what you ask for. Ask carefully!” –-TheTick, Eng-Tips
Did You get what You ASKED FOR?
Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]