but there are problems

Usually salespeople get commissions based on closing the sale, but there is a risk they will sell services that are difficult to fulfill, leaving the delivery team to pick up a mess. This tension is made worse because delivery teams are a big factor in selling follow-on work, yet aren't included in the commission.

Although this is most commonly a problem for services, it also happens with products, when post-sales people feel they are forced to try to fit a square product into a round need.

[removing commissions] takes away the scenario where the decision-making process for a salesperson is (or is perceived to be) influenced by personal commercial incentives. -- Gary Barnes, Head of Business Development in Europe

From a leader's perspective, it's better to move an experienced salesperson from easier work to harder tasks, or to get them to spend time mentoring less experienced staff. But doing these things makes it harder to make quota, so the salesperson's incentives aren't aligned with the needs of the office as a whole.
Monitoring sales figures is a significant drain on both the sales staff and management. Disputes over lead allocation, quota setting, and allocating sales can use up a lot of time and erodes trust. Certainly similar problems with occur with setting salaries, but arguments over commissions tend to be worse.

the amount of time spent by management defining and monitoring plans and more importantly by sales people optimizing plans and tracking them for their own cashflow purposes etc is unbelievable -- Trevor Mather, CEO

Commissions set up a competitive environment where salespeople are encouraged to look after their own commissions first, reducing cooperation between them.
Commissions can act as deterrent from selling innovative solutions. Such things, whether new products or unconventional approaches to service delivery, are often more difficult to sell. Therefore a salesperson can be put in a position where their income is at risk when when deciding whether to recommend an innovative approach.

We need our salesforce to be as enthusiastic around taking new innovations to market as it is about the proven money-making products like Go, Mingle and training courses -- Adrian Jones, VP of Global Sales for Studios

Even if these problems don't occur, the perception that they may happen erodes trust