Afghanistan as any other democracy has an elected president. It has a legitimate government that represents Afghanistan at the regional and international levels. As any government, it has to lead and manage the country. Therefore, Afghan government shall be involved in any process which is relevant to Afghanistan.
Afghan peace talk is one of the national processes of the country. Any deal on the peace talks, to be good or bad, has direct consequences on Afghan citizens. If Afghan government is not a central part of the peace talks, it will not be acceptable for the Afghan government and any decision made by such a process neither would be acceptable and nor it would be implementable in the future; Because when Afghan government is not involved as a central part of the peace talks, there is nearly no guarantee to implement the peace deal.
The Consequences of the Peace Talks Stumbling Afghan Government
This round of the talks shows that Khalilzad pursues to have the support of Pakistan in the peace talks. He actually wants Pakistan to make the Taliban engage fully in the talks with the United States to reach a peace deal. However, Khalilzad is pushing the same strategy to marginalize the Afghan government. In this case, even if there is a peace deal, it will not last and will not be implemented. 
Rejection of a peace deal by India
As the experience shows, India as one of the main players in Afghanistan is sidelined again from the talks. Considering the geopolitical location of Afghanistan, it is not logical to expect that India to accept a deal with Taliban. Because in this case Taliban as the proxy group of Pakistan will come to power and will threat the national security of India either directly or through its affiliate terrorist groups.
Emarat can lead to a new round of civil war in Afghanistan. Afghan people see no change in military and political approach of Taliban. As the group insists on its harsh ideology, it pursues establishment or revival of Emirat. How Afghan people from different walks will accept a discriminatory system that rejects them the human rights and basic rights? Taliban has ruled Afghanistan in the past. Taliban clearly called other ethnic groups as people of other countries and not Afghan citizens and wanted to force them to leave the country. Such group cannot provide an environment that all Afghans feel they are equal before the law. As a result, even if Afghans accept the Emarat due to fatigue of continued wars in the country, they will ultimately rise against the group. This will lead to a new civil war in Afghanistan.
All Afghans want peace. At the same time, they want a peace deal to ensure that the new Afghan democracy and its 18 years achievements will be preserved. Afghans want a peace deal to protect the Afghan constitution, civil liberties, basic rights and freedoms. Thus, Afghans want a peace and a political system that considers all Afghans as equal citizens of the country. Therefore, only an Afghan led and Afghan owned process under the leadership of Afghan government can ensure a lasting peace in the country.