PN, like EE are already part of the BT Group, so no merger needed!!
The Bean Counters may well squeeze more costs from them and so customer service may suffer, but BT uses PN as competition to TT and others, so they are likely to be around for as long as other ISP's undercut BT.
For what it is worth EE prices are,or can be as competitive, don't use the same in house network as PN, but do use the same as BTW, so don't have the same performance problems that PN do, of and their billing works too.