There wouldn’t be much policy reason for the feds to collect a provincial sales tax, without it being a VAT, just like the GST. They’re not interested just in harmonizing the tax base, but also the structure of the tax.
The idea of the HST is not just that the taxable items are the same, but that the sales taxes as currently structured distort the market and build taxes into the cost of goods. It’s argued that a VAT does not do this, that it doesn’t distort market prices as much and keeps the prices of goods more competitive. That was one of the arguments for the GST in the first place - it replaced a hidden federal manufacturing excise tax with a VAT tax. So the feds favour VAT taxes as a general economic policy, and are encouraging harmonization to achieve that policy.
I don’t know enough about the economics of taxation to say if the idea is sound, but that was the rationale. So I can’t see the feds being interested in the provinces just harmonizing the tax base; harmonization also includes the VAT concept.
Provincial sales taxes now do operate much like the old hidden federal manufacturing tax, since manufacturers pay the provincial tax on materials they buy to incorporate into their product. They naturally build the cost of the tax into the price of the product that the consumer pays, and then the consumer pays tax on that hidden tax. So not only does it drive the price up, there’s double-taxation. At least, that’s the argument. Again, I don’t know enough about the economics of taxation to say whether it’s so serious a problem as to justify switching to an HST.