Why did 'Kaikeyi' ask 14 years exile for Rama?

The following are the words of Manthara, the servant of Kaikeyi, when she explained her plan of action to Kaikeyi.

तौ वरौ याच भर्तारं भरतस्याभिषेचनम् |
प्रव्राजनं तु रामस्य त्वं वर्षाणि चतुर्दश || ९-२-२०

"You ask your husband as two boons, anointing Bharata for princely kingdom and sending Rama to exile for fourteen years."

चतुर्दश हि वर्षाणिरामे प्रव्राजिते वनम् |
प्रजाभावगतस्नेहः स्थिरः पुत्रो भविष्यति || ९-२-२१

If you send Rama to forest for fourteen years, your son Bharata will get intimate association in the hearts of the people and will get stabilised in kingdom.

Manthara was not talking about any custom or rule, which will make the possessor of the land for 12 or 13 or 14 years as de facto ruler of the land.

She was talking about possible intimate association in the hearts of the people by Bharata, in the absence of Sri Rama for 14 years, so that his rule can be stabilised.