In many presidential governments, president is not recommended or not allowed to appoint her/his own party member(s) who sit in national assembly. Why?
Why should a president be allowed to choose who sits in the legislature?
Most presidential systems are based on direct elections. The president is the single nationally elected official. Other officials are elected regionally or proportionally.
If the members of the national assembly are elected regionally, then the president doesn't choose them at all. A president can endorse but the real decision is in the hands of the voters. The United States (US) uses this kind of a system. Note also that the United Kingdom, which does not have a president, also uses this system.
If the party is elected proportionally, they can either be chosen via ranked voting or party list. In party list, you don't vote for individuals but by party. In ranked, you order a list of individuals by preference and rules are used to determine who wins. So ranked is similar to regional voting in that it puts voters in control.
Party list gives the power to select actual representatives to the party. The natural person to exercise that power is the party leader. A president is a natural party leader in those places that have one. But most party list assemblies have a prime minister instead of a president. This is because a prime minister is more consistent with the idea behind party list, that voters should empower parties who then empower individuals.
It's certainly not impossible to design a government where the president is directly elected and also in charge of a party list party. It's just a bit inconsistent. The usual reason to have them elected separately is to have the two act as checks and balances on each other. If you do that, then why reduce the checking power by putting part of the legislature under the control of the president?