Why can't Liton or Mithun keep wickets instead of Mushfiq?

It was deja vu all over again as Mushfiqur Rahim missed a chance to get a batsman out behind the stumps against New Zealand.
The drop of Jimmy Neesham led to Bangladesh losing their grip of the match and a flurry of misfields and catch drops ensued as the hosts rode their luck and reached home with five wickets and 10 balls to spare.
At that time New Zealand needed 101 runs from the last 15 overs and Neesham was the new man in the crease and Taskin Ahmed was unlucky to not have a wicket for his bowling effort. 
The next over, the 37th of the innings, Mahedi Hasan dropped the set Tom Latham who was on 58. 
The New Zealand skipper eventually went on to score a century and guide his team home but the story would have been different if those catches were taken. 
Mahedi though, was one of the bright spots for Bangladesh with the ball as he took two top-order wickets and had the hosts in trouble early on. 

Liton already keeps in Tests
There was a time when Mushfiq was the only keeper in the team's starting XI but the rise of Liton Das the batsman has raised questions over Mushfiq's eligibility as the primary keeper.
While Mushfiq has come to terms in red-ball cricket and given up the gloves to Liton, in limited-overs cricket, the senior statesman still takes charge behind the stumps.
With Mushfiq's latest blunder behind the stumps evoking memories of Bangladesh's match against New Zealand in the last World Cup, the cricketing fraternity has once again been abuzz with Mushfiq's keeping and why he still has the job. 
There have been numerous previous reports and Mushfiq himself has said that it helps his batting when he keeps as he can judge the pace and bounce of the wicket. 
But as we have seen in Tests, Mushfiq has made the adjustment and has maintained his batting form. 
His fielding may not be the best, but it certainly won't be as scrutinised as his wicketkeeping currently is. 
Mushfiq also looked rusty with the bat and played slow and shaky innings of 34 from 59 balls at a time when the team needed to up the ante.
Faster innings there could have set Bangladesh up with 15-20 more runs to play with. 

Tamim disappointed with dropped catches 
After the match, Bangladesh captain Tamim Iqbal didn't hide the fact that the dropped catches cost his team the win. 
"We should've won this game. Bowlers created chances, we couldn't hold on. The dropped catches, you know. When the situation comes, you have to do things 100%. I'm disappointed today," he said in the post-match presentation.
Tamim batted well after being put on to bat by New Zealand and scored 78 from 108 balls to set Bangladesh a platform to launch from. 
That eventually helped Bangladesh put on a score of 271 thanks to a quickfire 73 from 57 balls by Mohammad Mithun - his career-best.
Tamim also gave credit to his batsmen: "Batters did really well. It was a different surface, a bit slow, 271 was a decent score. And when the chances came, we couldn't hold on. It's quite disappointing. Mithun was fantastic." 
Tamim though, couldn't hide his disappointment of not being able to get their maiden win against New Zealand in New Zealand as they had a golden opportunity when the hosts were 53-3 in the 11th over. 
"Anyway, I thought it was a much-improved game. We are not here to improve our cricket but to win. See people will drop catches. It hurts. If we took our two chances, it was game on. People don't miss catches willingly, it happens to everyone. When the next chance comes, we need to grab with both hands. We just have to be positive in Wellington and give a crack at them again," Tamim said.
While Tamim is right, and the catches are not missed willingly, a decision can be made to make sure those 'catches' have a better chance of being caught. 

A case for Mithun
Liton, one may argue is a very good fielder as well, and his fielding comes in handy in white-ball cricket. 
In that case, Bangladesh also have Mithun who can keep wickets, although his place in the starting XI regularly remains in doubt. 
Mithun was also given a chance to try his hand at bowling in the game by captain Tamim and he did a decent job, but Mithun is primarily a wicket-keeping batsman.  
"I'm a wicket-keeper mainly and sometimes I bowl in the nets. I have bowled in a few games before and did pretty well. Maybe that's why the captain kept his faith in me," Mithun said in the post-match press conference. 
Tamim was proactive with his captaincy and field positioning and hardly put a foot wrong but one doubts if Tamim will use Mithun as a bowler on a more long-term basis.
He tried to mix things up by giving Mithun the ball and Tamim also affected the run out of the set batsman Devon Conway when he was on 72. 
But eventually, he will feel that a decision on the wicket-keeper needs to be made as soon as possible by the think tank. 
While the ODI series has been won by the hosts, Mithun feels that the team can take a lot of positives from this match. 
He also thinks that a win against New Zealand in New Zealand will be a big achievement for Bangladesh. 
"As a team, we want to win at least one match. I feel if we can win one match, it will be a big success for us. We will take the positives from this match and try to give our best in the next match. Hopefully, in the new match, we can get a different result," Mithun said.
But for a different result to happen, changes have to be made.