Why work on one thing at a time?

It is not possible to practice Samatha and Vipassana together. When it says practicing Samatha and Vipassana in tandem does not mean you practice them at the same time. However, you can interchange between the two. Generally in Vipassana, the first four stages (upto "He trains himself, 'I will breathe in calming bodily fabrication.'[3] He trains himself, 'I will breathe out calming bodily fabrication.'" are considered Samatha.

https://www.accesstoinsight.org/tipitaka/mn/mn.118.than.html

"Never half ass two things; whole ass one thing." - Ron Swanson

Put another way, there's only one road to enlightenment. The terrain of that road is less important than there only being one of them. What is your one road?

Case 48 of the Mumonkan
Kempõ's One Road

A monk asked Kempõ Oshõ, "It is written, 'Bhagavats in the ten directions. One straight road to Nirvana.'

I still wonder where the road can be."

Kempõ lifted his staff, drew a line, and said, "Here it is."

Later the monks asked the same question to Unmon, who held up his fan and said, "This fan jumps up to the thirty-third heaven and hits the nose of the deity Sakra Devanam Indra.

When you strike the carp of the eastern sea, the rain comes down in torrents."

Mumon's Comment

One, going to the bottom of the sea, lifts up clouds of dust; the other, on the top of the highest mountain, rises towering waves to wash the sky. One holding fast, the other letting go, each stretches out his hand to support the profound teaching. They are just like two riders starting from opposite ends of the course and meeting in the middle. But none on earth can be absolutely direct. When examined with a true eye, neither of these two great masters knows the road.

According to Abhidhamma, we can do only one thing at a time. (mind or thought-moment) However, as we are not paying attention we think they all happen at once. When you practice Satipathana you will understand this. When you practice Samatha you keep your attention only on the meditation object. In Vipassana you keep your attention only on one bodily activity (walking or breathing normally) but when you are experienced you extend to various daily activities.

The instruction to do "one thing at a time" is implied by the Buddha's praise of Sāriputta's practice, which was intense, deep and accomplished methodically one by one:

MN111:1.6: The Buddha said this: “Sāriputta is astute, mendicants. He has great wisdom, widespread wisdom, laughing wisdom, swift wisdom, sharp wisdom, and penetrating wisdom. For a fortnight he practiced discernment of phenomena one by one.

That fortnight was critical for Sariputta because it made him an arahant.

MN111:21.1: And if there’s anyone of whom it may be rightly said that they have attained mastery and perfection in noble ethics, immersion, wisdom, and freedom, it’s Sāriputta. And if there’s anyone of whom it may be rightly said that they’re the Buddha’s true-born child, born from his mouth, born of the teaching, created by the teaching, heir to the teaching, not the heir in material things, it’s Sāriputta.

Multi-tasking entails that one momentarily averts attention from one task in order to attend to other things in rapid succession. Clearly, driving while listening to the radio and thinking about what we want for dinner isn't practicing "one by one". Instead, conventional multi-tasking normally manifests as intermittent aversion to the unpleasant necessities while intermittently attending to the pleasant. The delusion that multi-tasking is effective is what makes it necessary to have laws that forbid dangerous multi-tasking such as texting and driving. Multi-tasking is therefore unskillful.

Practicing one by one is skillful.