And a currency based on a letter "S" can't be recognizable? What about $?
The dollar symbol can be written as an S with a complete strike through, or a partial strike-through (with just ticks on the top and the bottom). Likewise it can have a single or a double strike. All are representative of dollars. This shows that a currency does not need one absolute glyph. The strikethrough of the ASCII $ even changes between these four representations by just changing the font face.
The same dollar sign is used for currencies of many countries, not just the US. Besides dollars issued by other countries, pesos also use the $ glyph. Bitcoins and Baht sharing the same ฿ symbol is fine, as we see by example that varied world currencies already share the same symbol.
A double-strikethrough is very common in currency symbols, making the glyph easily recognizable as representative of money (₳ ₡ € ₱ ₩ ¥ etc). Therefore it would be ideal to migrate to a B of Bitcoin having double-ticks on the top and bottom to make the symbol more universally identifiable as currency but without being illegible from two complete strikethroughs. Barring this symbol being added to Unicode though, the ฿ shall do when represented in typography instead of logo form, and it can be handwritten with one slash instead of four.