I don't think we do, unsurprisingly. If we take the first eleven as being Lloris, Walker, Toby, Verts, Rose, Dier, Dembele, Lamela, Alli, Eriksen and Kane, then the second eleven we currently possess becomes Vorm, Trippier, CCV/Ball, Wimmer, Davies, Wanyama, Mason, Son, Onomah/Edwards, Chadli and Janssen. The remainder are the 3rd GK (McGee, presumably), Winks and Edwards, with whichever one of Ball and CCV that fails to make the cut as our 4th CB being the 26th man - beyond that, Sterling, Harrison, Walkes and Miller are also hanging around the first team at present, and the unwanted players (N'jie, Bentaleb, Fazio and Pritchard) have yet to be moved on.
In that 'second' eleven, we are critically weak in central midfield with Mason (given last season's evidence) and in attacking midfield with either Onomah or Edwards being the replacement for Alli - I would include the 4th CB position as another weakness, but in reality we're likely to see Dier or Wanyama drop back into that role if CCV or Ball don't make the cut. Now, in Mason's case, there's a case to be made (based on pre-season evidence) for Winks being the backup for Dembele instead of Mason, and it may also be the case that Mason recovers his form to an extent if he's over his injury.
But in central attacking midfield, we're definitely short if your aim is 2 strong players for each position - the impact of losing Alli and him being replaced by either Edwards or Onomah at this stage in their careers is not likely to be positive at all. Thus, it doesn't surprise me that we're on the lookout for another CAM - additionally, it ties in with a need identified by that article on tactics I linked a while back for a genuinely mobile CAM imbued with excellent close control that enables him to turn our transitions toward the opposition defense quicker than is currently the case (where controlling passes forward and *then* turning usually slows our attacks a bit).
And we're certainly not as stocked with strong CAMs as you're asserting. We have a base of good ones, and some very young, raw, promising backups - none in between.