The script below allows you to change Term Column Default Value in SharePoint Online using Client Side Object Model.  One of my client used an MMS Field in multiple libraries without using Site Column so I had to write this script to change the default value.  The script is iterating all sites and sub sites to find the fix the column.  It is a best practice to use Site Column.  You must use latest CSOM Components from Github for better performance.

$Creds = Get-Credential
Add-Type -Path “C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\16\ISAPI\Microsoft.SharePoint.Client.dll”
Add-Type -Path “C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\16\ISAPI\Microsoft.SharePoint.Client.Runtime.dll”
Add-Type -Path “C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\16\ISAPI\Microsoft.SharePoint.Client.Taxonomy.dll”

$Databases = $null
$Databases = @();

$ctx = New-Object Microsoft.SharePoint.Client.ClientContext(“https://tenant.sharepoint.com”)
#Authenticate
$credentials = New-Object Microsoft.SharePoint.Client.SharePointOnlineCredentials($Creds.UserName , $Creds.Password)
$ctx.Credentials = $credentials

#Fetch the users in Site Collection
$ctx.Load($ctx.Web)
$ctx.Load($ctx.Web.Webs)
$Lists = $ctx.Web.Lists
$ctx.Load($Lists)
$ctx.ExecuteQuery()

$taxStore = [Microsoft.SharePoint.Client.Taxonomy.TaxonomySession]::GetTaxonomySession($ctx) 
$ctx.Load($taxStore) 
$ctx.ExecuteQuery() 

$termStore = $taxStore.TermStores.GetByName(“Taxonomy_H2lgNrFxKmSlqqMA0l4JFw==”)
$Groups = $termStore.Groups 
$ctx.Load($termStore) 
$ctx.Load($Groups) 
$ctx.ExecuteQuery()

$Group = $Groups.GetByName(“Site Collection – tenant.sharepoint.com”) 
$termSet = $Group.TermSets.GetByName(“PrimaryTags”) 
$ctx.Load($termSet) 
$ctx.ExecuteQuery() 

foreach($List in $Lists)
{
  if($List.Hidden -eq $false)
  {
      if($Title -eq “Site Assets” -or $Title -eq “Master Page Gallery”)
      { continue }
      if($List.BaseType -eq “DocumentLibrary”)
      {
            $Fields = $List.Fields
            $ctx.Load($Fields)
            $ctx.ExecuteQuery()
            $PrimaryTag = $Fields | Where {$_.Title -eq “Primary Tag”}
            if($PrimaryTag)
            {
              $field = [Microsoft.SharePoint.Client.ClientContext].GetMethod(“CastTo”).MakeGenericMethod([Microsoft.SharePoint.Client.Taxonomy.TaxonomyField]).Invoke($ctx, $PrimaryTag)
              #$field.SspId = $termStore.Id
              #$field.TermSetId = $termSet.Id
              #$field.Update()
              #$ctx.ExecuteQuery()
            }
      }
  }
}
foreach($aWeb in $ctx.Web.Webs)
{
    $Lists = $aWeb.Lists
    $ctx.Load($Lists)
    $ctx.ExecuteQuery()
    foreach($List in $Lists)
    {
        $Title = $List.Title
        if($Title -eq “Site Assets” -or $Title -eq “Master Page Gallery”)
        { continue }
        if($List.BaseType -eq “DocumentLibrary”)
        {
            $Fields = $List.Fields
            $ctx.Load($Fields)
            $ctx.ExecuteQuery()
            $PrimaryTag = $Fields | Where {$_.Title -eq “Primary Tag”}
            if($PrimaryTag)
            {
              $field = [Microsoft.SharePoint.Client.ClientContext].GetMethod(“CastTo”).MakeGenericMethod([Microsoft.SharePoint.Client.Taxonomy.TaxonomyField]).Invoke($ctx, $PrimaryTag)
              if(!$field.DefaultValue.Contains(“#Project”))
              {
                $field.DefaultValue = “44;#Project Management|bf247376-f948-45b0-9dc6-69b94e9978f4”
                $field.Update()
              }
            }
            Write-Host $aSite.Url $List.Title $List.ItemCount
        }
    }
  }

Update: The script is also available

https://gallery.technet.microsoft.com/The-script-below-allows-31b6ee7f