what difference does it make if its a specialist batsman as a captain?
This is a philosophical discussion, therefore I am discussing ideal case scenario. But, it might happen that there is not better option than Babar.
Coming to the question, I'll respond it on 4 parts. History tells that specialist batsmen are often extremely defensive, safety first Captains and they try to use their influence to protect from defeat. That starts from playing on belters and picking 6/7 specialist batsmen in Test side. Cricket is a game of wickets - you have to find a way to get batsmen out and often specialist batsmen don't go for the kill at 50/50 situation. Whichever specialist batting Captain has done well were often leading a dominant side, where his job was more of house keeping. From Jardin/Bradman to Chappell, Lloyd, Tubby Taylor, Ponting, Smith, Strauss and now Kohli - they led solid sides, where they hardly were asked questions at 50/50 situations. Even Misbah & Cook were very good Captains at the venues their team were dominant. Unless the team is well settled & a solid bunch, batting Captains often make the game boring.
2nd point is the individual performance index. At the end of the day, apart from team's result, a Captain is responsible for own performance. Now, cricket batting is the most perfectionist job in sports - you make one mistake and you mind end effectively as 12th man for 5 days. For a batting Captain of an average side, pressure on own performance is extremely high. Statistically, if I take a 50 as minimum acceptable benchmark for a batsman, even the best are bound to fail 3 times out of 4. No one is going to give Captain a respite if he gets an unplayable ball for 29 (48). For a strong unit, it's not the biggest deal - once Mark Taylor had 18 Tests without a 50 (then he made 334*), but his team was doing fantastic. This is where bowling Captains, particularly all-rounders get lots of space, because bowling KPIs are measured in a different way - a bowling Captain can finish a Test for 1/100, but if he bowls well, he won't be criticized as much as a batting Captain going for 23 & 35. Besides, bowling Captains can find a space to hide - if he goes for runs, simply he can take him off for few overs and come back strong later; batting Captain can't go for an hour & come back. This actually allows bowling (all-rounder) Captain more space to relax when chips are down - isn't a big deal if you are leading a top side, but not for a side 7th in ranking.
For PAK specific, there are couple of reasons, I don't feel confident about batting Captain. First one is that, there is hardly any batsman who can lead from the front. Here, I am not talking about piling up runs like Azhar or Misbah. Last PAK Captain that was capable for that was Inzi & he led with full authority for 4 years - if Babar can replicate that, may be he can manage, time'll tell. 2nd factor is the core strategy of the team - PAK as a team can never play the game like what MSD does. That cat & mouse game is simply out of book. Play book for PAK is 10 wicket game - keep attacking & find a way to get batsmen out. This is where I found most batting Captains limited - they are not aggressive enough, neither have the bowling psyche, often misses the moments of killer instincts.
Historically, for most teams (apart from SRL, ZIM & BD - comfortably the 3 worst bowling sides in history), the historical best Captains were mostly all-rounders or batsmen who were decent bowlers. There are few exceptions (that's all-rounder being poor Captain), but these are the top Captains of most countries (my order, writing from memory with 1/2 misplaced, excluding current ones) -
AUS: Benaud, Ian Chappel, Armstrong, Taylor, Border, Jhonson, Monty Noble, Bradman, Darling, Vic Richardson, Simpson, Vic Trumper, Woodful (remember, ACB never appointed 2 of the best ever cricket minds for different reasons - Miller & Warne)
ENG: Tony Greig, Illingworth, Close, Ted Dexter, Jardin, Brearley, May, WG Grace, Walter Hammond, Strauss, Hutton, Willis, Nasser, Chapman, Douglas
WI: Worrell, Lloyd, Alexander, Viv, Sobers, Goddard, Stollmeyer, Denis Atkinson
SAF: Smith, Cronje, Bacher, Cheetham, Percey Sherwell, Goddard, Faulkner (Procter & Rice would have top class Captains)
NZ: Howarth, Fleming, Reid, Mac, Coney
IND: Pataudi, Ganguly, MSD, Lala, Kapil, Wadekar, Gavaskar
PAK: Imran, Kardar, Mushtaq, Wasim, Misbah, Intekhab, Javed
SRL: Arjuna, Wanrapura, Mahela, Mendis
Almost all of these Captains were accomplished First Class bowlers at least, most of them were Test all rounders or batting all-rounders. The fundamental of cricket leadership demands understanding of the moments to go for the kill - this is one solo reason, I supported MoHa as Captain over Misbah many, many times.
If there was no options, I probably would have gone for Babar obviously, but at the moment I'll go for Amir as Safr's deputy & may be Babar as Amir's deputy after 2019 WC, to take over after 2023 WC .... and Shadab becomes Babar's deputy to take over after 2027 WC for 4 to 8 years. It sounds a long pipe dream, but 10 years is too little time for such phasing out.