Not everything a church does has to have a Scriptural precedent, and just because it's not in Scripture doesn't mean it's automatically bad (Sunday school, the liturgical structure, using light bulbs instead of candles, grape juice rather than wine, these things simply develop or happen with time and circumstance, there's nothing intrinsically moral or immoral about them, although there's always going to be dissenters - after all, the Amish might have a bone to pick over the light bulbs). The Apostles themselves were itinerant, if you want to get technical, but that's a bit of a different situation to pastors. The fuller answer to the UMC's itinerant pastors is still probably going to be foreign or even scandalous to Baptist-type thinking.
Methodism originated in the Church of England in the 1700s, but due to the outbreak of the American Revolution, all of the priests in the colonies were recalled back to England and left no one to consecrate the elements for the Eucharist (since Methodists consider Communion to be a Sacrament, having properly ordained clergy to perform it is important). The first explicitly Methodist clergy were appointed and charged with serving in North America against this backdrop, and this action is what caused the split between the Church of England and the Methodists in the colonies. Because the new Methodist clergy were so few in number and the congregations so spread apart, they had to split their time amongst all the congregations in the area they served, and this is where the tradition of itinerant pastors in Methodism (not just the UMC; most, if not all, denominations in the Wesleyan family do this, to my knowledge) actually comes from. Eventually the number of clergy grew, and the travel distance between congregations they had to serve decreased, but the tradition of a pastor only serving a congregation for a time before moving onto another remained (at the discretion of the bishop, since making decisions about where priests/pastors serve has been in their job description since the Early Church period).
An important effect of it is also that because pastors are appointed from the top-down, there's far less of a threat of a pastor becoming beholden to the congregation in a way that becomes spiritually toxic or neglectful, since the congregation doesn't have the authority to throw out a pastor they've decided they have a problem with (like because the pastor doesn't just stick to telling the congregation what they want to hear instead of what they need to hear).
