The PPT presides over the Senate even less than the VP, so I'm not really sure what your point is.
The PPT is a ceremonial position based on seniority. Power in both chambers is vested in the elected leaders of the majority caucus - the Speaker in the House and the Majority Leader in the Senate.
But in theory, doesn't the PPT (or VP) have as much power over procedure as the Speaker, if one were to just look at this from a legal point of view.
In terms of the procedures of the bodies themselves NO!
The Senate filibuster is but one of the procedures in the Senate they empowers backbenchers as compared to their House counterparts. Originally one Senator could filibust anything without any opportunity of cloture, though of course it was only ever threatened as opposed to actually happening - this was more a historical abberation than anything else - Aaron Burr (VP in early 1800s) had the "Move the Previous Question" motion removed from the procedures of the Senate, meaning a majority could not force an end to debate because he saw it as pointless. Since it has never been fully reinstated, the power of a minority of Senators to stop the majority from acquiring power in the way that the House majority does continue to hold some sway.
The Speaker historically has done a very good job of centralising power to himself - their stranglehold on the Rules Committee (and therefore how each bill would be considered on the floor) was so strong at one point that Thomas Brackett Reed was referred to as Czar Reed at the end of the 19th century. Perhaps the most powerful was Speaker Cannon at the beginning of the 20th century who literally controlled everything - committee assignments, committee chairs, which committee got which bill. This all ended in 1910, when a cross party group managed to rest control of the Rules Committee from the Speaker and assert some independence for backbenchers, though this did swing back in the opposite direction in the 60s/70s when liberal Democrats removed power from conservative Dixiecrats who chaired committees and re-centralised it in the Speaker.
