I do not think that metals would influence the issues that you describe.
There are two distinct different types of issues and problem causes.
1. The first one is associated with metals (such as Al or Fe) buried in the silica. This is common with older "low purity" silicas. The metal ions are in the matrix and acidify surface silanols. This is why the older types of silica are more active towrds retention of bases and often give tailing. Since these metals are inside the matrix, they can not be removed.
Modern silicas are made from high-purity raw materials (i.e. organosilanes) that do not contain such impurities any more. With a very well designed and run process, metal impurities in these modern "high-purity" silicas practically do not exist any more. This is the primary reason why you get a much better peak shape for bases on these modern silicas.
2. However, there is another source of metal, and this is the column hardware and your stainless steel HPLC instrument. Actually, also your brown solvent bottles are a nice source of metals. These metal contaminants accumulate on the column during the operation. Contrary to the metals buried in the matrix, they sit on the surface and can be the cause of complexation, if you have analytes that are prone to do such things.
The only way to avoid this second type of metal contamination is to use a metal free system and to take the proper precautions with your source of mobile phase.
Unfortunately, there are lot of myths on this, but I hope that this clarifies things.